Download gem 8 mid-term review guide

Name: ______________________
Class: _________________
Date: _________
ID: A
GEM 8 MID-TERM REVIEW FOR WINTER BREAK
Multiple Choice
Identify the choice that best completes the statement or answers the question. Show all necessary work on rough work
paper. Write the answer selected on answer sheet given.
Complete the sentence.
____
1. 30 yd = ? ft
a.
b.
____
87
88
479.2
48
c.
d.
5
47.92
c.
d.
196
194
c.
d.
10.7
9.9
3. 78 in. ≈ ? cm
a.
b.
____
c.
d.
2. 4,792 cm = ? m
a.
b.
____
99
90
195
192
4. 9 m ≈ ? yd
a.
b.
12.4
11.2
Find the probability.
____
5. A person is randomly selected from a group consisting of 6 republicans, 20 democrats, and 19
independents. Find P(independent). Round to the nearest percent if necessary.
a.
b.
____
73%
44%
c.
d.
62%
42%
6. A marble is randomly selected from a bag containing 10 black, 14 white, and 7 clear marbles. Find
P(white). Round to the nearest percent if necessary.
a.
b.
32%
45%
c.
d.
65%
82%
c.
d.
2
0
Evaluate the expression.
____
7. x − 7 + y if x = 1 and y = 6.
a.
b.
–2
14
1
Name: ______________________
____
ID: A
8. 3ab + c if a = 6, b = −2 and c = 6.
a.
b.
–30
–26
c.
d.
31
–34
c.
d.
–1
4
c.
d.
–11
–4
Solve the equation.
____
9. −29 + y = −30
a.
b.
0
–59
____ 10. 3x = −24
a.
b.
–5
–8
Solve the inequality.
____ 11. 1 + g < 25
a.
b.
ÔÏ
Ô¸
ÌÔ g|g < 25 ˝Ô
Ó
˛
ÔÏ
Ô¸
ÌÔ g|g < 24 ˝Ô
Ó
˛
c.
d.
ÔÏ
Ô¸
ÌÔ g|g < 28 ˝Ô
Ó
˛
ÔÏ
Ô¸
ÌÔ g|g < 29 ˝Ô
Ó
˛
____ 12. −4t ≥ 36
a.
b.
ÔÏ
Ô¸
ÔÌÓ t|t ≥ 9 Ô˝˛
ÔÏ
Ô¸
ÔÌÓ t|t ≥ −10 Ô˝˛
c.
d.
2
ÔÏ
Ô¸
ÔÌÓ t|t ≥ −9 Ô˝˛
ÔÏ
Ô¸
ÔÌÓ t|t ≥ −4 Ô˝˛
Name: ______________________
ID: A
Find the point on a coordinate plane.
____ 13. Find the ordered pair for point B.
a.
b.
(1, –4)
(–1, –4)
c.
d.
(–1, 4)
(1, 4)
____ 14. Name the quadrant in which point (2, –3) is located.
a.
b.
III
IV
c.
d.
I
II
c.
d.
(4, –2)
(5, –4)
c.
d.
(0, 1)
(0, –1)
Solve the system of equations.
____ 15. −2x + y = −13
−2x + 5y = −33
a.
b.
(4, –5)
(5, –5)
____ 16. 6x + y = −1
−3x − 6y = 6
a.
b.
(3, 2)
(2, –1)
3
Name: ______________________
ID: A
Simplify.
____ 17.
75
a.
5
3
c.
15
b.
5
15
d.
5
37
c.
10
3
3
d.
10
6
c.
n
d.
p
c.
d.
H
JDB
____ 18.
12 •
a.
b.
6
25
2
Refer to Figure 1.
Figure 1
____ 19. Name a line that contains point J.
a.
b.
←⎯
⎯
→
DB
←⎯
⎯
→
GF
____ 20. Name the plane containing lines m and p.
a. n
b. GFC
____ 21. What is another name for line n?
a.
b.
line JB
←⎯
⎯
→
DC
____ 22. What is another name for line m?
a. line JG
b.
←⎯⎯
⎯
→
JGB
c.
←⎯
⎯
→
GF
d.
AC
c.
DB
d.
line JB
4
Name: ______________________
ID: A
____ 23. Name a line that contains point A.
a.
b.
←⎯
⎯
→
DC
m
c.
d.
←⎯
⎯
→
____ 25. Which of these is NOT a way to refer to line BD?
←⎯
→
JB
m
DB
←⎯
⎯
→
____ 24. Name a point NOT contained in AD or FG .
a. K
c.
b. A
d.
a.
b.
K
c.
d.
H
D
←⎯⎯
⎯
→
JDB
line JD
____ 26. Name three points that are collinear.
a.
b.
B, G, F
C, D, H
c.
d.
J, G, F
J, D, G
c.
d.
Q, L, M
R, S, K
____ 27. Name three points that are collinear.
a.
b.
M, L, R
L, P, T
5
Name: ______________________
ID: A
____ 28. Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a
figure for this relationship.
a.
c.
b.
d.
____ 29. Are points A, C, D, and F coplanar? Explain.
a.
b.
c.
d.
Yes; they all
No; they are
Yes; they all
No; three lie
lie on plane P .
not on the same line.
lie on the same face of the pyramid.
on the same face of the pyramid and the fourth does not.
6
Name: ______________________
ID: A
Refer to Figure 2.
Figure 2
____ 30. Name three collinear points.
a. B, L, D
b. C, L, B
c.
d.
K, A, C
D, F, G
____ 31. Where could you add point M on plane LBD so that D, B, and M would be collinear?
←⎯
⎯
→
a.
anywhere on DF
b.
anywhere on LD
←⎯
⎯
→
←⎯
⎯
→
c.
anywhere on BL
d.
anywhere on BD
←⎯
⎯
→
____ 32. Name a point that is NOT coplanar with G, A, and B.
a. K
c. C
b. D
d. F
____ 33. Name four points that are coplanar.
a. G, D, L, B
b. C, K, A, G
c.
d.
L, A, C, G
K, B, D, L
____ 34. Name an intersection of plane GFL and the plane that contains points A and C.
a. line LC
c. line AC
b. C
d. plane CAB
____ 35. Which plane(s) contain point K?
a. plane AGC
b. plane ADB, plane ALC
c.
d.
plane CAG, plane ABD
plane DBA
____ 36. Find the value of the variable and LN if M is between L and N.
LM = 8a, MN = 7a, LM = 56
a.
b.
a = 3.73, LN = 29.87
a = 7, LN = 105
c.
d.
7
a = 8, LN = 120
a = 7, LN = 49
Name: ______________________
ID: A
⎯⎯
⎯
→
In the figure, GK bisects ∠FGH.
____ 37. If m∠FGK = 7w + 3 and m∠FGH = 104, find w.
a. 7
c.
b. 14.43
d.
⎯
⎯
→
52
3.5
⎯⎯
→
⎯⎯
⎯
→
In the figure, KJ and KL are opposite rays. ∠1 ≅ ∠2 and KM bisects ∠NKL.
⎯⎯
⎯
→
____ 38. Which is NOT true about KM ?
a. ∠MKJ is acute.
b. ∠3 ≅ ∠MKL
c. Point M lies in the interior of ∠LKN.
d. It is an angle bisector.
____ 39. If ∠JKN is a right angle and m∠1 = 4t + 5, what is t?
a. 21.25
c. 43.75
b. 10
d. 45
8
Name: ______________________
ID: A
Use the figure to find the angles.
____ 40. Name two acute vertical angles.
a. ∠KQL, ∠KQM
b. ∠KQL, ∠IQH
c.
d.
∠GQI, ∠IQM
∠HQL, ∠IQK
____ 41. Name a pair of obtuse adjacent angles.
a. ∠KQG, ∠HQM
b. ∠GQL, ∠LQJ
c.
d.
∠GQI, ∠IQM
∠HQG, ∠IQH
____ 42. Name a linear pair.
a. ∠KQG, ∠HQM
b. ∠GQL, ∠LQJ
c.
d.
∠GQI, ∠IQM
∠LQG, ∠KQM
____ 43. Name an angle supplementary to ∠MQI.
a. ∠IQG
b. ∠GQL
c.
d.
∠MQK
∠IQH
____ 44. Name two obtuse vertical angles.
a. ∠KQL, ∠KQM
b. ∠KQL, ∠IQH
c.
d.
∠GQI, ∠IQM
∠HQL, ∠IQK
____ 45. Two angles are supplementary. One angle measures 26o more than the other. Find the measure of the
two angles.
a. 77, 103
c. 167, 193
b. 32, 58
d. 76, 104
9
Name: ______________________
ID: A
Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
____ 46.
a.
b.
triangle, convex, regular
triangle, convex, irregular
c.
d.
triangle, concave, irregular
quadrilateral, convex, irregular
a.
b.
quadrilateral, convex, regular
quadrilateral, concave, irregular
c.
d.
pentagon, convex, irregular
quadrilateral, convex, irregular
____ 47.
Find the length of each side of the polygon for the given perimeter.
____ 48. P = 72 units. Find the length of each side.
a.
b.
c.
d.
9 units, 36 units, 4 units, 23 units
8 units, 33 units, 4 units, 21 units
9 units, 35 units, 5 units, 23 units
10 units, 34 units, 6 units, 22 units
10
Name: ______________________
ID: A
Find the area of the figure.
____ 49.
a.
b.
7.13 cm
2
5.4 cm
2
2
c.
d.
71.3 cm
2
10.8 cm
____ 50. Name the bases of the solid.
a.
AB and CD
c.
ñA and ñB
b.
CB and BD
d.
ñC and ñD
c.
d.
UVZY and UVXW
UVXW and WXZY
____ 51. Name the bases of the prism.
a.
b.
ΔUWY and ΔVXZ
UVZY and WXZY
11
Name: ______________________
ID: A
Name the vertices of the solid.
____ 52.
a.
b.
A, C, I, G, E, and K
B, D, J, H, F, and L
c.
d.
A, B, C, and D
A, B, C, D, E, F, G, H, I, J, K, and L
Make a conjecture about the next item in the sequence.
____ 53. 1, 4, 16, 64, 256
a. 1024
b. 1025
c.
d.
4096
1022
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
____ 54. Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar.
a. False; the four points do not have to be in a straight line.
b. True
c. False; two points are always coplanar but four are not.
d. False; three points are always coplanar but four are not.
____ 55. Given: a concave polygon
Conjecture: It can be regular or irregular.
a. False; to be concave the angles cannot be congruent.
b. True
c. False; all concave polygons are regular.
d. False; a concave polygon has an odd number of sides.
____ 56. Given: Point B is in the interior of ∠ADC.
Conjecture: ∠ADB ≅ ∠BDC
a. False; m∠ADB may be obtuse.
b. True
c. False; just because it is in the interior does not mean it is on the bisecting line.
d. False; m∠ADB + m∠BDC = 90.
2
____ 57. Given: m + 6 = 10
Conjecture: m = 2
a. False; m = 4
b. True
c.
d.
12
False; m = 3
False; m = −2
Name: ______________________
ID: A
____ 58. Given: points R, S, and T
Conjecture: R, S, and T are coplanar.
a. False; the points do not have to be in a straight line.
b. True
c. False; the points to not have to form right angles.
d. False; one point may not be between the other two.
____ 59. Given: ∠ABC, ∠DBE are coplanar.
Conjecture: They are vertical angles.
a. False; the angles may be supplementary.
b. True
c. False; one angle may be in the interior of the other.
d. False; the angles may be adjacent.
____ 60. Given: Two angles are supplementary.
Conjecture: They are both acute angles.
a. False; either both are right or they are adjacent.
b. True
c. False; either both are right or one is obtuse.
d. False; they must be vertical angles.
____ 61. Given: ∠F is supplementary to ∠G and ∠G is supplementary to ∠H.
Conjecture: ∠F is supplementary to ∠H.
a. False; they could be right angles.
b. False; they could be congruent angles.
c. True
d. False; they could be vertical angles.
____ 62. Given:
Conjecture: ∠BCA ≅ ∠BAC
a. False; the angles are not vertical.
b. True
c. False; the angles are not complementary.
d. False; there is no indication of the measures of the angles.
13
Name: ______________________
ID: A
____ 63. Given: segments RT and ST; twice the measure of ST is equal to the measure of RT.
Conjecture: S is the midpoint of segment RT.
a. True
b. False; point S may not be on RT.
c. False; lines do not have midpoints.
d. False; ST could be the segment bisector of RT.
Use the following statements to write a compound statement for the conjunction or disjunction. Then find
its truth value.
p: An isosceles triangle has two congruent sides.
q: A right angle measures 90°
r: Four points are always coplanar.
s: A decagon has 12 sides.
____ 64. p ∧ s
a. An isosceles triangle has two congruent sides and a decagon has 12 sides; true.
b. An isosceles triangle has two congruent sides or a decagon has 12 sides; false.
c. An isosceles triangle has two congruent sides or a decagon has 12 sides; true.
d. An isosceles triangle has two congruent sides and a decagon has 12 sides; false.
14
Name: ______________________
ID: A
Complete the truth table.
____ 65.
p
q
r
T
T
T
T
T
F
T
F
T
F
∼q
r∧ ∼ q
F
F
F
F
15
Name: ______________________
ID: A
a.
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
F
F
F
T
T
T
F
F
F
T
F
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
T
F
F
T
T
F
F
F
F
T
F
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
T
T
F
F
T
T
F
T
F
F
F
T
T
T
F
F
F
T
F
F
F
T
T
T
F
F
F
T
F
b.
c.
16
Name: ______________________
ID: A
d.
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
F
F
F
T
T
F
F
F
F
T
F
Write the statement in if-then form.
____ 66. A counterexample invalidates a statement.
a. If it invalidates the statement, then there is a counterexample.
b. If there is a counterexample, then it invalidates the statement.
c. If it is true, then there is a counterexample.
d. If there is a counterexample, then it is true.
____ 67. Two angles measuring 90 are complementary.
a. If two angles measure 90, then two angles measure 90.
b. If two angles measure 90, then the angles are complementary.
c. If the angles are supplementary, then two angles measure 90.
d. If the angles are complementary, then the angles are complementary.
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is
false, find a counterexample.
____ 68. If you have a dog, then you are a pet owner.
a. If you are a pet owner, then you have a dog. True
b. A dog owner owns a pet. True
c. If you are a pet owner, then you have a dog. False; you could own a hamster.
d. If you have a dog, then you are a pet owner. True
____ 69. All Jack Russells are terriers.
a. If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier.
b. If it is a Jack Russell, then a dog is a terrier. True
c. If a dog is a terrier, then a dog is a terrier. True
d. All Jack Russells are terriers. True
17
Name: ______________________
ID: A
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false,
find a counterexample.
____ 70. People who live in Texas live in the United States.
a. People who do not live in the United States do not live in Texas. True
b. People who do not live in Texas do not live in the United States. False; they could
live in Oklahoma.
c. People who live in the United States live in Texas. False; they could live in
Oklahoma.
d. People who do not live in Texas live in the United States. True
____ 71. All quadrilaterals are four-sided figures.
a. All non-quadrilaterals are four-sided figures. False; a triangle is a non-quadrilateral.
b. All four-sided figures are quadrilaterals. True
c. No quadrilaterals are not four-sided figures. True
d. No four-sided figures are not quadrilaterals. True
____ 72. An equilateral triangle has three congruent sides.
a. A non-equilateral triangle has three congruent sides. False; an isosceles triangle has
two congruent sides.
b. A figure that has three non-congruent sides is not an equilateral triangle. True
c. A non-equilateral triangle does not have three congruent sides. True
d. A figure with three congruent sides is an equilateral triangle. True
____ 73. All country names are capitalized words.
a. All capitalized words are country names. False; the first word in the sentence is
capitalized.
b. All non-capitalized words are not country names. True
c. All non-country names are capitalized words. False; most of the words in the sentence
are non-capitalized words.
d. All non-country names are non-capitalized words. False; the first word in the
sentence is capitalized.
____ 74. Independence Day in the United States is July 4.
a. July 4 is not Independence Day in the United States. False; it is Independence Day.
b. Non-Independence Day in the United States is not July 4. True
c. Non-Independence Day in the United States is July 4. False; July 4 is Independence
Day in the United States.
d. Non-July 4 is not Independence Day in the United States. True
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or
false. If it is false, find a counterexample.
____ 75. If you are 16 years old, then you are a teenager.
a. If you are not a teenager, then you are not 16 years old. True
b. If you are not 16 years old, then you are not a teenager. False; you could be 17 years
old.
c. If you are not a teenager, then you are 16 years old. True
d. If you are a teenager, then you are 16 years old. False; you could be 17 years old.
18
Name: ______________________
ID: A
____ 76. A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.
a. A non-converse statement is not formed by exchanging the hypothesis and
conclusion of the conditional. True
b. A statement not formed by exchanging the hypothesis and conclusion of the
conditional is a converse statement. False; an inverse statement is not formed by
exchanging the hypothesis and conclusion of the conditional.
c. A non-converse statement is formed by exchanging the hypothesis and conclusion of
the conditional. False; an inverse statement is formed by negating both the
hypothesis and conclusion of the conditional.
d. A statement not formed by exchanging the hypothesis and conclusion of the
conditional is not a converse statement. True
____ 77. Two angles measuring 180 are supplementary.
a. Two angles not measuring 180 are supplementary. True
b. More than two angles measuring 180 are non-supplementary. True
c. Non-supplementary angles are not two angles measuring 180. True
d. Non-supplementary angles are two angles measuring 180. False; supplementary angles
must measure 180.
____ 78. If you have a gerbil, then you are a pet owner.
a. If you are not a pet owner, then you do not have a gerbil. True
b. If you do not have a gerbil, then you are not a pet owner. False; you could have a dog.
c. If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner
then you have no pets.
d. If you are not a gerbil, then you are not a pet owner. True
____ 79. Thanksgiving Day in the United States is November 25.
a. If it is not November 25, it is Thanksgiving Day in the United States. True
b. If it is not Thanksgiving Day in the United States, it is not November 25. False;
Thanksgiving Day could be another date in a different year so November 25 could be
not Thanksgiving Day.
c. If it is not November 25, it is not Thanksgiving Day in the United States. True
d. If it is not November 25, it is not Thanksgiving Day in the United States. False;
Thanksgiving Day could be another date in a different year.
Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the
Law of Syllogism. If it does, state which law was used. If it does not, write invalid.
____ 80. (1)
(2)
(3)
a.
b.
c.
You are in ninth grade.
People who are in ninth grade floss their teeth regularly.
You floss your teeth regularly.
yes; Law of Syllogism
invalid
yes; Law of Detachment
19
Name: ______________________
ID: A
In the figure below, points A, B, C, and F lie on plane
each statement is true.
P . State the postulate that can be used to show
____ 81. A and B are collinear.
a. If two points lie in a plane¸ then the entire line containing those points lies
in that plane.
b. Through any two points there is exactly one line.
c. If two lines intersect¸ then their intersection is exactly one point.
d. A line contains at least two points.
____ 82. Line AD contains points A and D.
a. If two lines intersect¸ then their intersection is exactly one point.
b. If two points lie in a plane¸ then the entire line containing those points lies
in that plane.
c. A line contains at least two points.
d. Through any two points¸ there is exactly one line.
Refer to the figure below.
____ 83. Name all planes intersecting plane CDI.
a. ABC, CBG, ADI, FGH
b. CBA, DAF, HGF
c.
d.
20
BAD, GFI, CBG, GFA
DAB, CBG, FAD
Name: ______________________
ID: A
____ 84. Name all segments parallel to GF.
a.
BC, AD, HI
c.
CD, HI
b.
AB, CD, HI
d.
AB, CD
____ 85. Name all segments skew to BC.
a.
FI, AD, FA, DI
c.
CD, AB, BG, CH
b.
FG, GH, HI, FI
d.
GF, HI, DI, AF
____ 86. Name all segments parallel to GH.
a.
BG, CH, FG, HI
c.
CD, AB, HI
b.
CD, BA, AF, DI
d.
BC, AD, FI
c.
d.
ADC, DIH, FIH, CHI
CDA, DAF, FGH, GBA
____ 87. Name all planes intersecting plane CHG.
a. BAD, CDI, FID, BGF
b. CBA, CDI, FIH, BAF
____ 88. Name all segments skew to HI.
a.
BC, AD, AF, BG
c.
AD, AB, BC, CD
b.
FI, GH, DI, CH
d.
BA, BG, AF, FG
____ 89. Name all segments parallel to AB.
a.
AD, BC, GH, FI
c.
CD, FG, HI
b.
DI, CH, GH, FI
d.
GH, AD, FI
____ 90. Name all segments skew to GF.
a.
BC, AD, DI, CH
c.
AD, AB, BC, CD
b.
FI, GH, DI, CH
d.
CD, CH, DI, HI
c.
d.
BCH, GFI, FGH, CBG
DCH, DAF, CBG, CBA
____ 91. Name all planes intersecting plane BAF.
a. BGH, CDA, FID, DIH
b. BCD, CHG, FID, FIH
____ 92. Name all segments parallel to BG.
a.
BA, FG, GH, BC
c.
AF, DI, CH
b.
AD, CD, HI, FI
d.
GH, AD, FI
21
Name: ______________________
ID: A
Identify the sets of lines to which the given line is a transversal.
____ 93. line j
a.
b.
c.
d.
lines m and n¸ n and o¸ m and o
lines m and p¸ n and o
lines i
lines m and n¸ n and o¸ m and o¸ m and p¸ n and p¸ o and p
____ 94. line a
a.
b.
c.
d.
lines c and b¸ f and d¸ c and f¸ c and d¸ b and d
lines a and b¸ a and c¸ a and d¸ a and f
lines f and d¸ c and f¸ c and d¸ b and d
lines c and b¸ f and d
←⎯
⎯
→
←⎯
→
Determine whether WX and YZ are parallel, perpendicular, or neither.
____ 95. W ÁÊË 0, − 3 ˜ˆ¯ , X ÁÊË −1, 5 ˜ˆ¯ , Y ÁÊË 2, 5 ˜ˆ¯ , Z ÁÊË −1, 2 ˜ˆ¯
a. parallel
b. perpendicular
c. neither
22
Name: ______________________
ID: A
Write an equation in point-slope form of the line having the given slope that contains the given point.
____ 96. m = −0.8, ÊÁË 14.5, 12.8 ˆ˜¯
a. y − 14.5 = −0.8(x − 12.8)
b. y − 12.8 = −0.8(x − 14.5)
c.
d.
y = −0.8x − 1.2
y + 12.8 = −0.8(x − 14.5)
Given the following information, determine which lines, if any, are parallel. State the postulate or
theorem that justifies your answer.
____ 97. ∠11 ≅ ∠2
a.
b.
c.
d.
c Ä d; congruent corresponding angles
a Ä b; congruent corresponding angles
c Ä d; congruent alternate interior angles
a Ä b; congruent alternate interior angles
23
Name: ______________________
ID: A
____ 98. ∠LHO ≅ ∠NKP
a.
b.
c.
d.
c Ä d; congruent corresponding angles
a Ä b; congruent corresponding angles
a Ä b; congruent alternate exterior angles
c Ä d; congruent alternate exterior angles
24
Name: ______________________
ID: A
Construct a line perpendicular to m through P. Then find the distance from P to m.
____ 99. Line m contains points ÊÁË 3, 1 ˆ˜¯ and ÊÁË 1, 1 ˆ˜¯ . Point P has coordinates ÊÁË 5, 2 ˆ˜¯ .
a.
c.
d=1
b.
d=2
d.
d=1
d=5
25
Name: ______________________
ID: A
____100. Line m contains points ÁÊË 3, − 3 ˜ˆ¯ and ÁÊË 0, 0 ˜ˆ¯ . Point P has coordinates ÁÊË 1, 2 ˜ˆ¯ .
a.
c.
d = 2.12
d = 2.55
b.
d.
d = 2.02
d = 2.12
Find the distance between the pair of parallel lines.
____101. y = 4x + 4
4x − y = 1
a. d = 1.64
b. d = 1.47
c.
d.
26
d = 1.21
d = 1.28
Name: ______________________
ID: A
Use a protractor to classify the triangle as acute, equiangular, obtuse, or right.
____102.
a.
b.
obtuse
right
c.
d.
equiangular and obtuse
equiangular and acute
c.
d.
m∠1 = 141, m∠2 = 84, m∠3 = 139
m∠1 = 141, m∠2 = 45, m∠3 = 141
Find each measure.
____103. m∠1, m∠2, m∠3
a.
b.
m∠1 = 135, m∠2 = 88, m∠3 = 139
m∠1 = 135, m∠2 = 84, m∠3 = 96
Name the congruent angles and sides for the pair of congruent triangles.
____104. ΔSKL ≅ ΔCFG
a. ∠S ≅ ∠G, ∠K ≅ ∠F, ∠L ≅ ∠C, SK ≅ GF, KL ≅ FC, SL ≅ GC
b.
∠S ≅ ∠F, ∠K ≅ ∠G, ∠L ≅ ∠C, SK ≅ FG, KL ≅ GC, SL ≅ FC
c.
∠S ≅ ∠C, ∠K ≅ ∠F, ∠L ≅ ∠G, SK ≅ CF, KL ≅ FG, SL ≅ CG
d.
∠S ≅ ∠G, ∠K ≅ ∠C, ∠L ≅ ∠F, SK ≅ GC, KL ≅ CF, SL ≅ GF
____105. ΔMGB ≅ ΔWYT
a. ∠M ≅ ∠T, ∠G ≅ ∠Y, ∠B ≅ ∠W, MG ≅ TY, GB ≅ YW, MB ≅ TW
b.
∠M ≅ ∠T, ∠G ≅ ∠W, ∠B ≅ ∠Y, MG ≅ TW, GB ≅ WY, MB ≅ TY
c.
∠M ≅ ∠W, ∠G ≅ ∠Y, ∠B ≅ ∠T, MG ≅ WY, GB ≅ YT, MB ≅ WT
d.
∠M ≅ ∠Y, ∠G ≅ ∠T, ∠B ≅ ∠W, MG ≅ YT, GB ≅ TW, MB ≅ YW
27
Name: ______________________
ID: A
Identify the congruent triangles in the figure.
____106.
a.
b.
ΔKLJ ≅ ΔONM
ΔKJL ≅ ΔOMN
c.
d.
ΔLJK ≅ ΔOMN
ΔJKL ≅ ΔONM
a.
b.
ΔSRT ≅ ΔWUV
ΔRST ≅ ΔWVU
c.
d.
ΔSTR ≅ ΔWVU
ΔTRS ≅ ΔWUV
____107.
Determine whether ΔPQR ≅ ΔSTU given the coordinates of the vertices. Explain.
____108. P ÊÁË 0, 3 ˆ˜¯ , Q ÊÁË 0, − 1 ˆ˜¯ , R ÊÁË −2, − 1 ˆ˜¯ , S ÊÁË 1, 2 ˆ˜¯ , T ÊÁË 1, − 2 ˆ˜¯ , U ÊÁË −1, − 2 ˆ˜¯
a. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
b. Yes; Each side of triangle PQR is the same length as the corresponding side of
triangle STU.
c. No; Two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.
d. Yes; Both triangles have an obtuse angle.
____109. P ÁÊË 3, − 2 ˜ˆ¯ , Q ÁÊË 1, 2 ˜ˆ¯ , R ÁÊË −1, 4 ˜ˆ¯ , S ÁÊË −4, − 3 ˜ˆ¯ , T ÁÊË −2, 1 ˜ˆ¯ , U ÁÊË 0, 3 ˜ˆ¯
a. Yes; Each side of triangle PQR is the same length as the corresponding side of
triangle STU.
b. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
c. No; Two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.
d. Yes; Both triangles have three sides.
28
Name: ______________________
ID: A
____110. P ÁÊË −2, − 3 ˜ˆ¯ , Q ÁÊË −4, 2 ˜ˆ¯ , R ÁÊË −1, 4 ˜ˆ¯ , S ÁÊË 2, − 3 ˜ˆ¯ , T ÁÊË 1, 2 ˜ˆ¯ , U ÁÊË −1, 3 ˜ˆ¯
a. Yes; Each side of triangle PQR is the same length as the corresponding side of
triangle STU.
b. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
c. No; Neither side has a right angle.
d. Yes; Two sides of triangle PQR and angle PQR are the same measure as the
corresponding sides and angle of triangle STU.
____111. P ÊÁË −3, 2 ˆ˜¯ , Q ÊÁË −2, − 3 ˆ˜¯ , R ÊÁË −1, 4 ˆ˜¯ , S ÊÁË 2, 4 ˆ˜¯ , T ÊÁË 3, − 1 ˆ˜¯ , U ÊÁË 4, 6 ˆ˜¯
a. Yes; Both triangles have three acute angles.
b. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
c. No; Two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.
d. Yes; Each side of triangle PQR is the same length as the corresponding side of
triangle STU.
____112. P ÊÁË 4, 0 ˆ˜¯ , Q ÊÁË 2, − 3 ˆ˜¯ , R ÊÁË −1, 4 ˆ˜¯ , S ÊÁË −1, − 4 ˆ˜¯ , T ÊÁË 1, − 1 ˆ˜¯ , U ÊÁË 4, 6 ˆ˜¯
a. Yes; Two sides of triangle PQR and angle PQR are the same measure as the
corresponding sides and angle of triangle STU.
b. Yes; Each side of triangle PQR is the same length as the corresponding side of
triangle STU.
c. No; One of the triangles is obtuse.
d. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
Refer to the figure. ΔARM, ΔMAX, and ΔXFM are all isosceles triangles.
____113. If m∠FXA = 96, what is m∠FMR?
a. 96
b. 134
c.
d.
152
138
____114. If m∠FMR = 155, what is m∠FMX?
a. 45
b. 55
c.
d.
65
35
29
Name: ______________________
ID: A
____115. Triangle FJH is an equilateral triangle. Find x and y.
7
5
7
5
a.
x=
, y = 16
c.
x=
, y = 14
b.
x = 7, y = 16
d.
x = 7, y = 14
____116. Triangle RSU is an equilateral triangle. RT bisects US. Find x and y.
a.
x = 3, y = 18
c.
x = 3, y = 42
b.
x=
d.
x=
12 , y = 42
12 , y = 18
Identify the type of congruence transformation.
____117.
a.
b.
reflection
translation
c.
d.
30
rotation
not a congruence transformation
Name: ______________________
ID: A
____118.
a.
b.
reflection or translation
translation only
c.
d.
rotation or translation
rotation only
Position and label the triangle on the coordinate plane.
____119. right isosceles ΔABC with congruent sides AB and AC a units long
a.
c.
b.
d.
31
Name: ______________________
ID: A
____120. right ΔHJK with non-hypotenuse side HJ twice as long as non-hypotenuse side HK a units
a.
c.
b.
d.
____121. isosceles ΔLMN with base LN 2b units long
a.
c.
b.
d.
32
Name: ______________________
ID: A
____122. equilateral ΔLMN with height a units and one-half base LN b units
a.
c.
b.
d.
____123. right ΔABC with hypotenuse AB, leg AC 4a units long, and leg BC one-fourth the other leg
a.
c.
b.
d.
33
Name: ______________________
ID: A
____124. one-half equilateral triangle with SU bisecting the triangle at height a units and base ST 2b units
a.
c.
b.
d.
____125. right ΔLMN with hypotenuse MN 5a units and base LM 3a units
a.
c.
b.
d.
34
Name: ______________________
ID: A
____126. equilateral ΔZYX with height c units and base XY 2d units
a.
c.
b.
d.
____127. isosceles ΔABC with CD half the length of the base and bisecting the base
a.
c.
b.
d.
35
Name: ______________________
ID: A
____128. isosceles ΔFGH with GI twice the length of the base and bisecting the base
a.
c.
b.
d.
Determine the relationship between the measures of the given angles.
____129. ∠PTC, ∠VPT
a.
b.
∠PTC > ∠VPT
∠PTC < ∠VPT
c.
∠PTC = ∠VPT
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no.
Explain.
____130. 3, 9, 10
a. Yes; the third side is the longest.
b. No; the sum of the lengths of two sides is not greater than the third.
c. No; the first side is not long enough.
d. Yes; the sum of the lengths of any two sides is greater than the third.
____131. 9.2, 14.5, 17.1
a. Yes; the third side is the longest.
b. No; the first side is not long enough.
c. Yes; the sum of the lengths of any two sides is greater than the third.
d. No; the sum of the lengths of two sides is not greater than the third.
36
Name: ______________________
ID: A
____132. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if
necessary.
a. 2160
c. 154.3
b. 25.7
d. 360
____133. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.
a. 1260
c. 360
b. 140
d. 40
Complete the statement about parallelogram ABCD.
____134. AD ≅
a.
CG; Opposite sides of parallelograms are congruent.
b.
BC; Diagonals of parallelograms bisect each other.
c.
BC; Opposite sides of parallelograms are congruent.
d.
CG; Diagonals of parallelograms bisect each other.
Refer to parallelogram ABCD to answer to following questions.
____135. Are the diagonals congruent? Justify your answer.
a. Yes; Both diagonals have a length of 2 34 .
b.
Yes; Both diagonals have a length of 6
2.
c.
d.
Yes; Both diagonals have a length of 3 2 .
No; The lengths of the diagonals are not the same.
37
Name: ______________________
ID: A
Refer to parallelogram ABCD to answer the following questions.
____136. Are the diagonals congruent? Justify your answer.
a. Yes; Both diagonals have a length of 73 .
b.
Yes; Both diagonals have a length of
13 .
c.
d.
Yes; Both diagonals have a length of 18.25 .
No; The lengths of the diagonals are not the same.
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.
____137. A(3, − 9), B(10, 1), C(4, 10), D(−9, 3); Distance and Slope Formulas
a. No; The opposite sides are not congruent and do not have the same slope.
b. Yes; The opposite sides do not have the same slope.
c. No; The opposite sides do not have the same slope.
d. Yes; The opposite sides are not congruent and do not have the same slope.
Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a
square. List all that apply.
____138. A(5, 10), B(4, 10), C(4, 9), D(5, 9)
a. square; rectangle; rhombus
b. rhombus
c.
d.
square
rectangle
____139. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
a.
b.
65
32.5
c.
d.
38
28
3
Name: ______________________
ID: A
____140. For trapezoid JKLM, A and B are midpoints of the legs. Find AB.
a.
b.
23
8
c.
d.
35
46
Position and label each quadrilateral on the coordinate plane.
____141. rectangle with side length b units and height d units
a.
c.
b.
d.
39
Name: ______________________
ID: A
____142. square with side length b units
a.
c.
b.
d.
____143. trapezoid with height d units, bases b and b + k units
a.
c.
b.
d.
40
Name: ______________________
ID: A
____144. parallelogram with side length d units and height b units
a.
c.
b.
d.
____145. rectangle with side length 2k units and height 4k
a.
c.
b.
d.
41
Name: ______________________
ID: A
____146. square with side length 4k units
a.
c.
b.
d.
____147. rectangle with side length 4k units and height 2k units
a.
c.
b.
d.
42
Name: ______________________
ID: A
____148. square with side length 2k units
a.
c.
b.
d.
____149. isosceles trapezoid with height c units, bases 4d units and 2d units
a.
c.
b.
d.
43
Name: ______________________
ID: A
____150. isosceles trapezoid with height c units, bases 8d units and 4d units
a.
c.
b.
d.
44
ID: A
GEM 8 MID-TERM REVIEW FOR WINTER BREAK
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
TOP:
KEY:
4. ANS:
OBJ:
TOP:
KEY:
5. ANS:
OBJ:
KEY:
6. ANS:
OBJ:
KEY:
7. ANS:
OBJ:
TOP:
8. ANS:
OBJ:
TOP:
9. ANS:
OBJ:
KEY:
10. ANS:
OBJ:
KEY:
11. ANS:
OBJ:
KEY:
12. ANS:
OBJ:
KEY:
13. ANS:
OBJ:
KEY:
B
PTS: 1
DIF: Basic
REF: Lesson 0-1
0-1.1 Convert units of measure within the customary and metric systems.
Changing units of measure within systems.
KEY: Units of Measure |Within Systems
D
PTS: 1
DIF: Basic
REF: Lesson 0-1
0-1.1 Convert units of measure within the customary and metric systems.
Changing units of measure within systems.
KEY: Units of Measure |Within Systems
A
PTS: 1
DIF: Basic
REF: Lesson 0-2
0-2.1 Convert units of measurement between the customary and metric systems.
Changing units of measure between systems.
Units of Measure |Between Systems
D
PTS: 1
DIF: Basic
REF: Lesson 0-2
0-2.1 Convert units of measurement between the customary and metric systems.
Changing units of measure between systems.
Units of Measure |Between Systems
D
PTS: 1
DIF: Basic
REF: Lesson 0-3
0-3.1 Find the probability of simple events.
TOP: Simple probability.
probability
B
PTS: 1
DIF: Basic
REF: Lesson 0-3
0-3.1 Find the probability of simple events.
TOP: Simple probability.
probability
D
PTS: 1
DIF: Basic
REF: Lesson 0-4
0-4.1 Use the order of operations to evaluate algebraic expressions.
Algebraic expressions.
KEY: Algebraic expressions
A
PTS: 1
DIF: Basic
REF: Lesson 0-4
0-4.1 Use the order of operations to evaluate algebraic expressions.
Algebraic expressions.
KEY: Algebraic expressions
C
PTS: 1
DIF: Basic
REF: Lesson 0-5
0-5.1 Use algebra to solve linear equations.
TOP: Linear equations.
Linear Equations
B
PTS: 1
DIF: Basic
REF: Lesson 0-5
0-5.1 Use algebra to solve linear equations.
TOP: Linear equations.
Linear Equations
B
PTS: 1
DIF: Basic
REF: Lesson 0-6
0-6.1 Use algebra to solve linear inequalities.
TOP: Linear inequalities.
Linear Inequalities
C
PTS: 1
DIF: Basic
REF: Lesson 0-6
0-6.1 Use algebra to solve linear inequalities.
TOP: Linear inequalities.
Linear Inequalities
A
PTS: 1
DIF: Basic
REF: Lesson 0-7
0-7.1 Name and graph points in the coordinate plane. TOP: Ordered pairs.
ordered pair | x-coordinate | y-coordinate | quadrant | origin
1
ID: A
14. ANS:
OBJ:
KEY:
15. ANS:
OBJ:
TOP:
16. ANS:
OBJ:
TOP:
17. ANS:
OBJ:
TOP:
KEY:
18. ANS:
OBJ:
TOP:
KEY:
19. ANS:
B
PTS: 1
DIF: Basic
REF: Lesson 0-7
0-7.1 Name and graph points in the coordinate plane. TOP: Ordered pairs.
ordered pair | x-coordinate | y-coordinate | quadrant | origin
A
PTS: 1
DIF: Basic
REF: Lesson 0-8
0-8.1 Use graphing, substitution, and elimination to solve systems of linear equations.
Systems of linear equations.
KEY: system of equations | substitution | elimination
D
PTS: 1
DIF: Basic
REF: Lesson 0-8
0-8.1 Use graphing, substitution, and elimination to solve systems of linear equations.
Systems of linear equations.
KEY: system of equations | substitution | elimination
A
PTS: 1
DIF: Basic
REF: Lesson 0-9
0-9.1 Evaluate square roots and simplify radical expressions.
Square roots and simplifying radicals.
Product Property | Quotient Property
C
PTS: 1
DIF: Basic
REF: Lesson 0-9
0-9.1 Evaluate square roots and simplify radical expressions.
Square roots and simplifying radicals.
Product Property | Quotient Property
A
←⎯
⎯
→
Line n contains points A, D, and C. Line p contains points G and F. Only line DB contains point J.
Feedback
A
B
C
D
Correct!
Is point J on that line?
What points are on that line?
What points are on that line?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
STA: LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify and model points, lines, and planes.
KEY: Points | Lines | Planes
20. ANS: B
A plane is a flat surface made up of points. A plane is named by a capital script letter or by the letters
naming three noncollinear points.
Feedback
A
B
C
D
Is that the way you name a plane?
Correct!
Is that the way you name a plane?
Do three collinear points name a plane?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
TOP: Identify and model points, lines, and planes.
2
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Points | Lines | Planes
ID: A
21. ANS: B
A line is made up of points with an arrowhead at each end. A, D, and C are points on line n. A line is
←⎯
⎯
→
represented by ‘line DC’ or DC but not just DC.
Feedback
A
B
C
D
Are those points on line n?
Correct!
Are those points on line n?
Is that how a line is named?
PTS:
OBJ:
TOP:
22. ANS:
A line
1
DIF: Average
REF: Lesson 1-1
1-1.1 Identify and model points, lines, and planes.
STA: LA.1112.1.6.1 | MA.912.G.8.1
Identify and model points, lines, and planes.
KEY: Points | Lines | Planes
D
is made up of points and has no thickness or width. It is drawn with an arrowhead at each end. J,
←⎯
⎯
→
D, and B are points on line m. A line is represented by ‘line JD’ or JD but not just JD.
Feedback
A
B
C
D
Are those points on line m?
Is that how you name a line?
Is that how you name a line?
Correct!
PTS:
OBJ:
TOP:
23. ANS:
1
DIF: Average
REF: Lesson 1-1
1-1.1 Identify and model points, lines, and planes.
Identify and model points, lines, and planes.
A
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Points | Lines | Planes
←⎯
⎯
→
Line m contains points J, D, and B. Line p contains points G and F. Only line DC contains point A.
Feedback
A
B
C
D
Correct!
Is point A on that line?
Is that a line?
What points are on that line?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
TOP: Identify and model points, lines, and planes.
3
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Points | Lines | Planes
ID: A
24. ANS: C
←⎯
⎯
→
←⎯
⎯
→
The points not contained in AD or FG are J, B, and H. K is the plane.
Feedback
A
B
C
D
Is that a point or the plane?
Is that point on one of the lines listed?
Correct!
Is that point on one of the lines listed?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
STA: LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify and model points, lines, and planes.
KEY: Points | Lines | Planes
25. ANS: C
The proper way to refer to a line is any 2 points on the line with an arrow above them or “line
such-and-such”, where “such-and-such” is any 2 points on the line. Using three letters is not correct.
Feedback
A
B
C
D
Does line BD contain point J?
Does that line contain points B and D?
Correct!
Are points J and D on line BD?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
TOP: Identify and model points, lines, and planes.
26. ANS: A
Collinear points are points on the same line.
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Points | Lines | Planes
Feedback
A
B
C
D
Correct!
Are those points on the same line?
What does collinear mean?
Are those points on the same line?
PTS: 1
DIF: Average
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Collinear Points
REF: Lesson 1-1 OBJ: 1-1.2 Identify collinear points.
TOP: Identify collinear points.
4
ID: A
27. ANS: A
Collinear points are points on the same line.
Feedback
A
B
C
D
Correct!
Are those points on the same line?
Are those points on the same line?
What does collinear mean?
PTS: 1
DIF: Average
REF: Lesson 1-1 OBJ: 1-1.2 Identify collinear points.
STA: LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify collinear points.
KEY: Collinear Points
28. ANS: C
Points that lie on the same plane are said to be coplanar. Lines are made up of points. If line c intersects
only with line b, then lines a and c must be parallel.
Feedback
A
B
C
D
Does line c intersect line a?
What does coplanar mean?
Correct!
Are lines a and c parallel?
PTS:
STA:
KEY:
29. ANS:
Points
fourth
1
DIF: Average
REF: Lesson 1-1 OBJ: 1-1.3 Identify coplanar points.
LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify coplanar points.
Coplanar Points | Intersecting Lines | Lines in Space
D
that lie on the same plane are said to be coplanar. Three points are always coplanar but if the
point is not on the same plane with the first three, they are not all coplanar.
Feedback
A
B
C
D
Do all four points lie on the same plane? Which plane?
Do all four points lie on the same plane? Which plane?
What does coplanar mean?
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-1 OBJ: 1-1.3 Identify coplanar points.
STA: LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify coplanar points.
KEY: Coplanar Points | Intersecting Lines | Lines in Space
5
ID: A
30. ANS: D
Collinear points are points on the same line.
Feedback
A
B
C
D
You are looking for collinear points, not coplanar points.
Are those points on the same line?
What is meant by collinear?
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
TOP: Identify intersecting lines and planes in space.
31. ANS: D
Collinear points are points on the same line.
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Planes | Planes in Space
Feedback
A
B
C
D
What plane are you working with?
Which points should be collinear?
What does collinear mean?
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
TOP: Identify intersecting lines and planes in space.
32. ANS: C
Coplanar points are points that lie on the same plane.
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Planes | Planes in Space
Feedback
A
B
C
D
Is K in a different plane?
What plane are you working with?
Correct!
What plane are you working with?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
TOP: Identify intersecting lines and planes in space.
6
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Planes | Planes in Space
ID: A
33. ANS: B
Coplanar points are points that lie on the same plane.
Feedback
A
B
C
D
What is the definition of coplanar?
Correct!
Are all the points in the same plane?
What is the definition of coplanar?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
TOP: Identify intersecting lines and planes in space.
34. ANS: A
The intersection of two planes is a line.
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Planes | Planes in Space
Feedback
A
B
C
D
Correct!
Can the intersection of two planes be a point?
Is point A on plane GFL?
Can the intersection of two planes be a plane?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
STA: LA.1112.1.6.1 | MA.912.G.8.1
TOP: Identify intersecting lines and planes in space.
KEY: Planes | Planes in Space
35. ANS: C
In this diagram two planes contain point K—the front end of the prism and the top face of the prism.
Feedback
A
B
C
D
Is there another one?
Is point K on plane ALC?
Correct!
Is there another one?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
TOP: Identify intersecting lines and planes in space.
7
STA: LA.1112.1.6.1 | MA.912.G.8.1
KEY: Planes | Planes in Space
ID: A
36. ANS: B
Solve for a first using the two values of LM. LN = LM + MN. Solve for LN.
Feedback
A
B
C
D
Which two segments in the question are the same?
Correct!
Which two segments in the question are the same?
Which segment are you solving for?
PTS:
STA:
KEY:
37. ANS:
1
DIF: Basic
REF: Lesson 1-2 OBJ: 1-2.3 Compute with measures.
MA.912.G.1.2 | MA.912.G.8.6
TOP: Compute with measures.
Measurement | Compute Measures
A
⎯⎯
⎯
→
104
Since GK bisects ∠FGH, x = y and 7w + 3 =
. Solve for w.
2
Feedback
A
B
C
D
Correct!
You are given the measure of ∠FGH, not ∠KGH.
You are not finding the measure of ∠FGK. You are finding w.
Why did you divide by 2?
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.3 Identify and use congruent angles.
TOP: Identify and use congruent angles.
KEY: Angles | Congruent Angles | Congruency
38. ANS: A
∠MKH > 90, so it is obtuse.
STA: MA.912.G.1.2 | MA.912.G.8.4
Feedback
A
B
C
D
Correct!
If answer d is true, then this must be true.
Being in the interior means being between the two end rays of an angle.
If answer b is true, then this must be true.
PTS: 1
DIF: Basic
REF: Lesson 1-4
OBJ: 1-4.4 Identify and use the bisector of an angle.
TOP: Identify and use the bisector of an angle.
8
STA: MA.912.G.1.2 | MA.912.G.8.4
KEY: Angle Bisectors
ID: A
39. ANS: B
m∠JKN = 2 ( m∠1 ) = 90
Feedback
A
B
C
D
What is the definition of "right angle"?
Correct!
What is the definition of "right angle"?
You are solving for t.
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.4 Identify and use the bisector of an angle.
STA: MA.912.G.1.2 | MA.912.G.8.4
TOP: Identify and use the bisector of an angle.
KEY: Angle Bisectors
40. ANS: B
Vertical angles are two nonadjacent angles formed by two intersecting lines. Acute angles measure less
than 90 degrees.
Feedback
A
B
C
D
You are looking for vertical angles, not adjacent angles.
Correct!
You are looking for vertical angles, not a linear pair.
What is the definition of acute?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
41. ANS: B
Adjacent angles are two angles that lie in the same plane, have a common vertex, and a common side,
but no common interior points. Obtuse angles measure greater than 90 degrees.
Feedback
A
B
C
D
You are looking for adjacent angles, not vertical angles.
Correct!
You are looking for adjacent angles, not a linear pair.
What is the definition of obtuse?
PTS:
OBJ:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 1-5
1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
9
ID: A
42. ANS: C
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Feedback
A
B
C
D
You are looking for a linear pair, not vertical angles.
You are looking for a linear pair, not just adjacent angles.
Correct!
You are looking for a linear pair which, by definition, must be adjacent.
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
43. ANS: A
Supplementary angles are two angles whose measures have a sum of 180.
Feedback
A
B
C
D
Correct!
What is the definition of supplementary?
Do the measures have a sum of 180 degrees?
What is the definition of supplementary?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
44. ANS: D
Vertical angles are two nonadjacent angles formed by two intersecting lines. Obtuse angles measure
greater than 90 degrees.
Feedback
A
B
C
D
You are looking for vertical angles, not adjacent angles.
What is the definition of obtuse?
You are looking for vertical angles, not a linear pair.
Correct!
PTS:
OBJ:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 1-5
1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
10
ID: A
45. ANS: A
Supplementary angles are two angles whose measures have a sum of 180.
Feedback
A
B
C
D
Correct!
What is the definition of supplementary?
What is the sum of those two measures?
Is the measure of one angle 26 more than the other?
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
STA: MA.912.G.1.2 | MA.912.G.8.2
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
46. ANS: B
Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the
polygon, then it is concave. Otherwise it is convex.
A convex polygon in which all the sides are congruent and all the angles are congruent is called a regular
polygon.
Feedback
A
B
C
D
If it is regular the angles and sides would all be congruent.
Correct!
If it is concave, lines drawn from the segments would pass through the polygon.
Count the number of sides.
PTS: 1
DIF: Basic
REF: Lesson 1-6 OBJ: 1-6.2 Name polygons.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
TOP: Name polygons.
KEY: Polygons | Name Polygons
47. ANS: D
Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the
polygon, then it is concave. Otherwise it is convex.
A convex polygon in which all the sides are congruent and all the angles are congruent is called a regular
polygon.
Feedback
A
B
C
D
If it is regular, the angles and sides would all be congruent.
If it is concave, lines drawn from the segments would pass through the polygon.
Count the number of sides.
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-6 OBJ: 1-6.2 Name polygons.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
TOP: Name polygons.
KEY: Polygons | Name Polygons
11
ID: A
48. ANS: C
Perimeter is the sum of the sides.
Feedback
A
B
C
D
Did you find the value of r?
What is the value of r?
Correct!
What is the sum of the sides?
PTS:
OBJ:
STA:
TOP:
49. ANS:
1
DIF: Average
REF: Lesson 1-6
1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
Find the perimeters of polygons. KEY: Perimeter | Polygons
A
The area of a rectangle is the product of its length and width.
A = l×w
Feedback
A
B
C
D
Correct!
You need to multiply not add.
Place the decimal in the correct position.
You have calculated the perimeter.
PTS: 1
DIF: Basic
REF: Lesson 1-6
OBJ: 1-6.5 Find area of two-dimensional figures.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
TOP: Find area of two-dimensional figures.
KEY: Area | Two-Dimensional Figures
50. ANS: C
This solid is a cylinder. The bases of a cylinder are circles. In this cylinder, the circular bases are centered
at points A and B, thus the correct answer is ñA and ñB.
Feedback
A
B
C
D
The bases of a cylinder are circles, not segments.
The bases of a cylinder are circles, not segments.
Correct!
Those are the wrong centers for the circular bases.
PTS: 1
DIF: Basic
REF: Lesson 1-7
OBJ: 1-7.1 Identify three-dimensional figures.
TOP: Identify three-dimensional figures.
12
STA: MA.912.G.7.1 | MA.912.G.7.2
KEY: Three-Dimensional Figures
ID: A
51. ANS: A
The bases of a prism are congruent, parallel polygons. Here those polygons are the right triangles UWY
and VXZ.
Feedback
A
B
C
D
Correct!
Are those polygons congruent and parallel?
The bases of a prism are congruent, parallel polygons.
Are those polygons parallel?
PTS: 1
DIF: Basic
REF: Lesson 1-7
OBJ: 1-7.1 Identify three-dimensional figures.
STA: MA.912.G.7.1 | MA.912.G.7.2
TOP: Identify three-dimensional figures.
KEY: Three-Dimensional Figures
52. ANS: D
In a solid, all points that represent intersections of edges are vertices. Therefore all of the points shown
are vertices.
Feedback
A
B
C
D
That’s only half right.
That’s only half right.
There are more vertices than that.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 1-7
OBJ: 1-7.1 Identify three-dimensional figures.
STA: MA.912.G.7.1 | MA.912.G.7.2
TOP: Identify three-dimensional figures.
KEY: Three-Dimensional Figures
53. ANS: A
Start with 1. Add, subtract, or multiply the same number to each number to get the next one.
Feedback
A
B
C
D
Correct!
What operations are involved?
Didn’t you carry the conjecture too far?
Check your math.
PTS: 1
DIF: Basic
REF: Lesson 2-1
OBJ: 2-1.1 Make conjectures based on inductive reasoning.
TOP: Make conjectures based on inductive reasoning.
13
STA: LA.910.1.6.5 | MA.912.G.8.3
KEY: Inductive Reasoning | Conjectures
ID: A
54. ANS: D
Coplanar points always lie in the same plane. Three points are always coplanar but four are not.
Feedback
A
B
C
D
What does coplanar mean?
What does coplanar mean?
Are more than two points always coplanar?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
55. ANS: A
Concave polygons must be irregular. This means all sides and angles are not congruent.
Feedback
A
B
C
D
Correct!
What is the definition of concave?
Is that counterexample correct?
What is the definition of concave?
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
56. ANS: C
Angles are congruent only if their measures are equal. Point B may be closer to line AD or line DC so the
measures would not be equal.
Feedback
A
B
C
D
What is the definition of congruent?
What is the definition of congruent?
Correct!
Would that be a counterexample?
PTS: 1
DIF: Basic
STA: LA.910.1.6.5 | MA.912.G.8.3
KEY: Counterexamples
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
TOP: Find counterexamples.
14
ID: A
57. ANS: D
Because m is squared in the example, m could be positive or negative.
Feedback
A
B
C
D
Subtract 6 from both sides.
What about negative numbers?
Subtract 6 from both sides.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
58. ANS: B
Coplanar points always lie in the same plane. Three points are always coplanar but four are not.
Feedback
A
B
C
D
What does coplanar mean?
Correct!
What does coplanar mean?
Would the points have to be in the same plane?
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
59. ANS: C
Just because two angles share a common point does not mean they are vertical. They could be nearly
adjacent or one could be in the interior of the other one.
Feedback
A
B
C
D
What is a vertical angle?
What is a vertical angle?
Correct!
What is a vertical angle?
PTS: 1
DIF: Basic
STA: LA.910.1.6.5 | MA.912.G.8.3
KEY: Counterexamples
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
TOP: Find counterexamples.
15
ID: A
60. ANS: C
If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the
other acute.
Feedback
A
B
C
D
What is the definition of supplementary?
What is the definition of supplementary?
Correct!
What is the definition of supplementary?
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
61. ANS: B
If two angles are supplementary their measures total 180. ∠F could only be supplementary to ∠H if they
are both right angles.
Feedback
A
B
C
D
What is the definition of supplementary?
Correct!
What is the definition of supplementary?
What is the definition of supplementary?
PTS: 1
DIF: Basic
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
STA: LA.910.1.6.5 | MA.912.G.8.3
TOP: Find counterexamples.
KEY: Counterexamples
62. ANS: D
Unless there are specific angle measures mentioned, even though the angles in the picture may look
congruent you cannot assume that they are congruent.
Feedback
A
B
C
D
What is the definition of congruent?
What is the definition of congruent?
What is the definition of congruent?
Correct!
PTS: 1
DIF: Basic
STA: LA.910.1.6.5 | MA.912.G.8.3
KEY: Counterexamples
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
TOP: Find counterexamples.
16
ID: A
63. ANS: B
Even though they have a common point, the two segments do not have to be on the same line.
Feedback
A
B
C
D
What is the definition of midpoint?
Correct!
What is the definition of midpoint?
What is the definition of midpoint?
PTS: 1
DIF: Basic
STA: LA.910.1.6.5 | MA.912.G.8.3
KEY: Counterexamples
64. ANS: D
Two or more statements can be joined to
statement formed by joining two or more
statement formed by joining two or more
The symbol for logical or is ∨.
REF: Lesson 2-1 OBJ: 2-1.2 Find counterexamples.
TOP: Find counterexamples.
form a compound statement. A conjunction is a compound
statements with the word and. A disjunction is a compound
statements with the word or. The symbol for logical and is ∧.
Feedback
A
B
C
D
How many sides does a decagon have?
What is the symbol for logical and?
What is the symbol for logical and?
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-2
OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions.
STA: MA.912.D.6.1
TOP: Determine truth values of conjunctions and disjunctions.
KEY: Truth Values | Conjunctions | Disjunctions
65. ANS: A
The first statement column in a truth table contains half Ts, half Fs, grouped together. The second
statement column in a truth table contains the same, but they are grouped by half the number that the
first column was. The third statement column contains the same but they are grouped by half the number
that the second column was. Use the truth values of the first three columns to determine the truth values
for the last two columns. The symbol for not is ∼. The symbol for logical and is ∧.
Feedback
A
B
C
D
Correct!
Check the values for the last two columns carefully.
Do your statement columns show every possible T and F combination?
Check the values for the last two columns carefully.
PTS: 1
DIF: Average
STA: MA.912.D.6.1
KEY: Truth Tables
REF: Lesson 2-2 OBJ: 2-2.2 Construct truth tables.
TOP: Construct truth tables.
17
ID: A
66. ANS: B
The format of if-then form is “If hypothesis, then conclusion.”
Feedback
A
B
C
D
Which part is the hypothesis?
Correct!
What is the hypothesis?
What is the conclusion?
PTS: 1
DIF: Basic
REF: Lesson 2-3
OBJ: 2-3.1 Analyze statements in if-then form.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Analyze statements in if-then form.
KEY: If-Then Statements | Hypotheses | Conclusions
67. ANS: B
The format of if-then form is “If hypothesis, then conclusion.”
Feedback
A
B
C
D
What is the conclusion?
Correct!
Which part is the hypothesis?
What is the hypothesis?
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.1 Analyze statements in if-then form.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Analyze statements in if-then form.
KEY: If-Then Statements | Hypotheses | Conclusions
68. ANS: C
The converse of a conditional statement ÁÊË p → q ˜ˆ¯ exchanges the hypothesis and conclusion of the
conditional. It is also known as q → p.
Feedback
A
B
C
D
Check the statement again.
Check the statement again.
Correct!
What is the definition of converse?
PTS:
OBJ:
STA:
TOP:
1
DIF: Basic
REF: Lesson 2-3
2-3.2 Write the converse of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
Write the converse of if-then statements.
18
KEY: Converse | If-Then Statements
ID: A
69. ANS: A
The converse of a conditional statement ÊÁË p → q ˆ˜¯ exchanges the hypothesis and conclusion of the
conditional. It is also known as q → p.
Feedback
A
B
C
D
Correct!
What is the definition of converse?
Check the statement again.
Check the statement again.
PTS: 1
DIF: Basic
REF: Lesson 2-3
OBJ: 2-3.2 Write the converse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the converse of if-then statements.
KEY: Converse | If-Then Statements
70. ANS: B
The inverse is negating both the hypothesis and conclusion of the conditional.
∼p→∼q
Feedback
A
B
C
D
Remember ∼ p → ∼ q.
Correct!
Is that the converse?
Remember ∼ p → ∼ q.
PTS: 1
DIF: Basic
REF: Lesson 2-3
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the inverse of if-then statements.
KEY: Inverse | If-Then Statements
71. ANS: C
The inverse is negating both the hypothesis and conclusion of the conditional.
∼p→∼q
Feedback
A
B
C
D
Remember ∼ p → ∼ q.
Remember ∼ p → ∼ q.
Correct!
Remember ∼ p → ∼ q.
PTS:
OBJ:
STA:
TOP:
1
DIF: Average
REF: Lesson 2-3
2-3.3 Write the inverse of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
Write the inverse of if-then statements.
19
KEY: Inverse | If-Then Statements
ID: A
72. ANS: C
The inverse is negating both the hypothesis and conclusion of the conditional.
∼p→∼q
Feedback
A
B
C
D
Remember ∼ p → ∼ q.
Remember ∼ p → ∼ q.
Correct!
Is that the converse?
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the inverse of if-then statements.
KEY: Inverse | If-Then Statements
73. ANS: D
The inverse is negating both the hypothesis and conclusion of the conditional.
∼p→∼q
Feedback
A
B
C
D
Is that the converse?
Remember ∼ p → ∼ q.
Remember ∼ p → ∼ q.
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the inverse of if-then statements.
KEY: Inverse | If-Then Statements
74. ANS: B
The inverse is negating both the hypothesis and conclusion of the conditional.
∼p→∼q
Feedback
A
B
C
D
Remember ∼ p → ∼ q.
Correct!
Remember ∼ p → ∼ q.
Remember ∼ p → ∼ q.
PTS:
OBJ:
STA:
TOP:
1
DIF: Average
REF: Lesson 2-3
2-3.3 Write the inverse of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
Write the inverse of if-then statements.
20
KEY: Inverse | If-Then Statements
ID: A
75. ANS: A
In the contrapositive you negate both the hypothesis and conclusion of the converse statement.
∼q→∼p
Feedback
A
B
C
D
Correct!
Is that the inverse?
Remember ∼ q → ∼ p.
Remember ∼ q → ∼ p.
PTS: 1
DIF: Basic
REF: Lesson 2-3
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the contrapositive of if-then statements.
KEY: Contrapositive | If-Then Statements
76. ANS: D
In the contrapositive you negate both the hypothesis and conclusion of the converse statement.
∼q→∼p
Feedback
A
B
C
D
Remember ∼ q → ∼ p.
Remember ∼ q → ∼ p.
Remember ∼ q → ∼ p.
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the contrapositive of if-then statements.
KEY: Contrapositive | If-Then Statements
77. ANS: C
In the contrapositive you negate both the hypothesis and conclusion of the converse statement.
∼q→∼p
Feedback
A
B
C
D
Is this true?
Remember ∼ q → ∼ p.
Correct!
Remember ∼ q → ∼ p.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 2-3
2-3.4 Write the contrapositive of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
Write the contrapositive of if-then statements.
Contrapositive | If-Then Statements
21
ID: A
78. ANS: A
In the contrapositive you negate both the hypothesis and conclusion of the converse statement.
∼q→∼p
Feedback
A
B
C
D
Correct!
Is that the inverse?
Remember ∼ q → ∼ p.
Remember ∼ q → ∼ p.
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the contrapositive of if-then statements.
KEY: Contrapositive | If-Then Statements
79. ANS: C
Based on logic rather than general knowledge. In the contrapositive you negate both the hypothesis and
conclusion of the converse statement. ∼ q → ∼ p
Feedback
A
B
C
D
Remember ∼ q → ∼ p.
Is that the inverse?
Correct!
Use logic and given statement.
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
TOP: Write the contrapositive of if-then statements.
KEY: Contrapositive | If-Then Statements
80. ANS: C
The Law of Syllogism states, “If p → q and q → r are true, then p → r is also true.”
The Law of Detachment states, “If p → q is true and p is true, then q is also true.”
Feedback
A
B
C
What are the definitions of the two Laws of Reasoning?
What are the definitions of the two Laws of Reasoning?
Correct!
PTS:
OBJ:
STA:
KEY:
1
DIF: Average
REF: Lesson 2-4
2-4.1 Use the Law of Detachment and the Law of Syllogism.
MA.912.D.6.4
TOP: Use the Law of Detachment and the Law of Syllogism.
Law of Detachment | Law of Syllogism
22
ID: A
81. ANS: B
Postulates:
1. Through any two points, there is exactly one line.
2. Through any three points not on the same line, there is exactly one plane.
3. A line contains at least two points.
4. A plane contains at least three points not on the same line.
5. If two points lie in a plane, then the entire line containing those points lies in that plane.
6. If two lines intersect, then their intersection is exactly one point.
7. If two planes intersect, then their intersection is a line.
Feedback
A
B
C
D
Does that apply?
Correct!
Is that a postulate?
Does that fit the situation?
PTS: 1
DIF: Average
REF: Lesson 2-5
OBJ: 2-5.1 Identify and use basic postulates about points, lines, and planes.
STA: MA.912.D.6.4 | MA.912.G.8.1 | MA.912.G.8.5
TOP: Identify and use basic postulates about points, lines, and planes.
KEY: Points | Lines | Planes
82. ANS: C
Postulates:
1. Through any two points, there is exactly one line.
2. Through any three points not on the same line, there is exactly one plane.
3. A line contains at least two points.
4. A plane contains at least three points not on the same line.
5. If two points lie in a plane, then the entire line containing those points lies in that plane.
6. If two lines intersect, then their intersection is exactly one point.
7. If two planes intersect, then their intersection is a line.
Feedback
A
B
C
D
Is that a postulate?
Does that fit the situation?
Correct!
Does that apply?
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 2-5
2-5.1 Identify and use basic postulates about points, lines, and planes.
MA.912.D.6.4 | MA.912.G.8.1 | MA.912.G.8.5
Identify and use basic postulates about points, lines, and planes.
Points | Lines | Planes
23
ID: A
83. ANS: A
Planes that intersect have a common line.
Feedback
A
B
C
D
Correct!
This plane has four lines to intersect with other planes.
Do they all intersect plane CDI in a line?
This plane has four lines to intersect with other planes.
PTS: 1
DIF: Basic
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
84. ANS: B
Coplanar segments that do not intersect are parallel.
Feedback
B
Are those parallel to GF?
Correct!
C
Are those all of the segments parallel to GF?
D
Are those all of the segments parallel to GF?
A
PTS: 1
DIF: Basic
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
85. ANS: D
Skew lines do not intersect and are not coplanar.
Feedback
A
B
C
D
Are any of those segments in the same plane as BC?
Skew lines are not coplanar.
Do any of those segments intersect BC?
Correct!
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 3-1
3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
24
ID: A
86. ANS: D
Coplanar segments that do not intersect are parallel.
Feedback
A
B
C
D
Parallel lines do not intersect.
Parallel lines are coplanar.
Those segments are parallel to which line?
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
87. ANS: B
Planes intersect in a line.
Feedback
A
B
C
D
Do they all intersect plane CHG in a line?
Correct!
Is that all?
Do they all intersect plane CHG in a line?
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
88. ANS: A
Skew lines do not intersect and are not coplanar.
Feedback
A
B
C
D
Correct!
Skew lines do not intersect.
Skew lines are not coplanar.
Skew lines are not coplanar.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 3-1
3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
25
ID: A
89. ANS: C
Coplanar segments that do not intersect are parallel.
Feedback
A
B
C
D
Parallel lines do not intersect.
Parallel lines are coplanar.
Correct!
Those segments are parallel to which line?
PTS: 1
DIF: Basic
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
90. ANS: A
Skew lines do not intersect and are not coplanar.
Feedback
A
B
C
D
Correct!
Skew lines do not intersect.
Skew lines are not coplanar.
Skew lines are not coplanar.
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
STA: LA.1112.1.6.1 | MA.912.G.1.3
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
91. ANS: B
Planes intersect in a line.
Feedback
A
B
C
D
Do they all intersect plane CHG in a line?
Correct!
Is that all?
Do they all intersect plane CHG in a line?
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 3-1
3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
26
ID: A
92. ANS: C
Coplanar segments that do not intersect are parallel.
Feedback
A
B
C
D
Parallel lines do not intersect.
Parallel lines are coplanar.
Correct!
Those segments are parallel to which line?
PTS:
OBJ:
STA:
TOP:
KEY:
93. ANS:
A line
1
DIF: Basic
REF: Lesson 3-1
3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
D
that intersects two or more lines in a plane at different points is called a transversal.
Feedback
A
B
C
D
What about line p?
You need every combination of the lines.
What is the definition of transversal?
Correct!
PTS:
OBJ:
STA:
KEY:
94. ANS:
A line
1
DIF: Basic
REF: Lesson 3-1
3-1.2 Name angles formed by a pair of lines and a transversal.
LA.1112.1.6.1 | MA.912.G.1.3
TOP: Name angles formed by a pair of lines and a transversal.
Transversals | Two Lines and a Transversal | Angles
A
that intersects two or more lines in a plane at different points is called a transversal.
Feedback
A
B
C
D
Correct!
What is the definition of transversal?
You need every combination of lines.
You need every combination of the lines.
PTS:
OBJ:
STA:
KEY:
1
DIF: Average
REF: Lesson 3-1
3-1.2 Name angles formed by a pair of lines and a transversal.
LA.1112.1.6.1 | MA.912.G.1.3
TOP: Name angles formed by a pair of lines and a transversal.
Transversals | Two Lines and a Transversal | Angles
27
ID: A
95. ANS: C
ÊÁ y − y ˆ˜
ÁË 2
1˜
¯
The formula for slope is Ê
. If the slopes are the same they are parallel. If the product of the two
ÁÁ x − x ˜ˆ˜
1¯
Ë 2
slopes is –1, they are perpendicular.
Feedback
A
B
C
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-3
OBJ: 3-3.2 Use slope to identify parallel and perpendicular lines.
STA: MA.912.G.8.3
TOP: Use slope to identify parallel lines and perpendicular lines.
KEY: Parallel Lines | Perpendicular Lines | Slope
96. ANS: B
The point-slope form is y − y 1 = m ÊÁÁË x − x 1 ˆ˜˜¯ . Point ÊÁÁË x 1 , y 1 ˆ˜˜¯ is a point through which the line passes.
Feedback
A
B
C
D
Did you switch x and y?
Correct!
Is that point-slope form?
Be careful with signs.
PTS: 1
DIF: Average
REF: Lesson 3-4
OBJ: 3-4.2 Solve problems by writing equations.
TOP: Solve problems by writing equations.
28
STA: MA.912.G.8.2
KEY: Solve Problems | Write Equations
ID: A
97. ANS: C
Postulates and theorems:
If corresponding angles are congruent, then lines are parallel.
If given a line and a point not on the line, then there exists exactly one line through the point that is
parallel to the given line.
If alternate exterior angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
If alternate interior angles are congruent, then lines are parallel.
If two lines are perpendicular to the same line, then lines are parallel.
Feedback
A
B
C
D
What kind of angles are those?
What kind of angles are those?
Correct!
Which lines are parallel?
PTS: 1
DIF: Basic
REF: Lesson 3-5
OBJ: 3-5.1 Recognize angle conditions that occur with parallel lines.
STA: MA.912.G.1.2
TOP: Recognize angle conditions that occur with parallel lines.
KEY: Angles | Parallel Lines
98. ANS: C
Postulates and theorems:
If corresponding angles are congruent, then lines are parallel.
If given a line and a point not on the line, then there exists exactly one line through the point that is
parallel to the given line.
If alternate exterior angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
If alternate interior angles are congruent, then lines are parallel.
If two lines are perpendicular to the same line, then lines are parallel.
Feedback
A
B
C
D
What kind of angles are those?
What kind of angles are those?
Correct!
Which lines are parallel?
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 3-5
3-5.1 Recognize angle conditions that occur with parallel lines.
MA.912.G.1.2
Recognize angle conditions that occur with parallel lines.
Angles | Parallel Lines
29
ID: A
99. ANS: B
The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m.
y2 − y1
The slope of line m is
, which is 0. This is a horizontal line. The perpendicular line, then would
x2 − x1
be a vertical line, x = 5, going through point P. The point on m where line p intersects it would be
ÊÁ 5, 1 ˆ˜ . Use the Distance Formula to find the distance from point P to the point on m that intersects line
Ë
¯
p.
d=
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2
ÁË 2
ÁË 2
1˜
1˜
¯
¯
d=
(5 − 5 ) + (2 − 1 )
2
2
d=1
Feedback
A
B
C
D
Remember it is (x, y).
Correct!
You want the distance to line m.
You want the distance to line m.
PTS:
OBJ:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 3-6
3-6.1 Find the distance between a point and a line.
Find the distance between a point and a line.
Distance | Distance Between a Point and a Line
30
STA: MA.912.G.1.2
ID: A
100. ANS: C
ÊÁ 0 − ( −3 ) ˆ˜
ÁË
˜¯
The slope of line m is
, which is Ê
= −1. The equation for line m is
x2 − x1
ÁÁ 0 − ( 3 ) ˜ˆ˜
Ë
¯
Ê
ˆ
y − ( −3 ) = −1 ÁÁË x − ( 3 ) ˜˜¯ or y = −1x + ( 0 ) . The slope of a line p perpendicular to m has the negative
1
reciprocal to the equation of line m. The perpendicular line, then would be , going through point P.
1
1 ÊÁ
ˆ
The line containing point P would be y − ( 2 ) = ÁË x − ( 1 ) ˜˜¯ or y = 1x + ( 1 ) . You need to find a common
1
point for the two lines, so set the equations equal to each other.
1x + ( 1 ) = −1x + ( 0 )
y2 − y1
x = −0.5
y = 0.5
Use the Distance Formula from that common point to point P.
d=
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2
ÁË 2
ÁË 2
1˜
1˜
¯
¯
d=
ÊÁ 1 − ( −0.5 ) ˆ˜ 2 + ÊÁ 2 − ( 0.5 ) ˆ˜ 2
ÁË
˜¯
ÁË
˜¯
d = 2.12
Feedback
A
B
C
D
You want the distance to line m.
Did you use the distance formula?
Correct!
Remember it is (x, y).
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 3-6
3-6.1 Find the distance between a point and a line.
Find the distance between a point and a line.
Distance | Distance Between a Point and a Line
31
STA: MA.912.G.1.2
ID: A
101. ANS: C
The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines.
1
The perpendicular line containing the y-intercept would be y = − x + 4. You need to find a common
4
point for the two lines, so set the equations equal to each other.
1
− x + 4 = 4x − 1
4
x = 1.18
y = 3.71
Use the Distance Formula from that common point to the y-intercept of the first line.
d=
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2
ÁË 2
ÁË 2
1˜
1˜
¯
¯
d=
( 1.18 − 0 ) + ( 3.71 − 4 )
2
2
d = 1.21
Feedback
A
B
C
D
Construct a perpendicular line and find the intersection point on each parallel line.
Construct a perpendicular line and find the intersection point on each parallel line.
Correct!
Construct a perpendicular line and find the intersection point on each parallel line.
PTS: 1
DIF: Average
REF: Lesson 3-6
OBJ: 3-6.2 Find the distance between parallel lines.
STA: MA.912.G.1.2
TOP: Find the distance between parallel lines.
KEY: Distance | Parallel Lines | Distance Between Parallel Lines
102. ANS: D
An acute triangle has 3 acute angles.
An obtuse triangle has one obtuse angle.
A right triangle has one right angle.
Feedback
A
B
C
D
Check for congruent sides and measure angles.
Check for congruent sides and measure angles.
Check for congruent sides and measure angles.
Correct!
PTS: 1
DIF: Average
REF: Lesson 4-1
OBJ: 4-1.1 Identify and classify triangles by angles.
TOP: Identify and classify triangles by angles.
32
STA: MA.912.G.4.1 | MA.912.G.8.6
KEY: Triangles | Classify Triangles
ID: A
103. ANS: C
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the
sum of the measures of the two remote interior angles.
Feedback
A
B
C
D
What is the sum of the measures of the angles in a triangle?
Did you use the Exterior Angle Theorem?
Correct!
Use the Exterior Angle Theorem.
PTS: 1
DIF: Average
REF: Lesson 4-2
OBJ: 4-2.2 Apply the Exterior Angle Theorem.
STA: MA.912.G.2.2 | MA.912.G.8.5 | MA.912.D.6.4 | MA.912.G.8.2
TOP: Apply the Exterior Angle Theorem.
KEY: Exterior Angle Theorem
104. ANS: C
The corresponding sides and angles can be determined from any congruence statement by following the
order of the vertices.
Feedback
A
B
C
D
The corresponding sides and angles can be determined from any congruence
statement by following the order of the vertices.
The corresponding sides and angles can be determined from any congruence
statement by following the order of the vertices.
Correct!
Did you follow the order of the vertices?
PTS: 1
DIF: Basic
REF: Lesson 4-3
OBJ: 4-3.1 Name and label corresponding parts of congruent triangles.
STA: MA.912.G.4.4 | MA.912.G.4.6
TOP: Name and label corresponding parts of congruent triangles.
KEY: Corresponding Parts | Congruent Triangles
105. ANS: C
The corresponding sides and angles can be determined from any congruence statement by following the
order of the vertices.
Feedback
A
B
C
D
Did you follow the order of the vertices?
The corresponding sides and angles can be determined from any congruence
statement by following the order of the vertices.
Correct!
Did you follow the order of the vertices?
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 4-3
4-3.1 Name and label corresponding parts of congruent triangles.
MA.912.G.4.4 | MA.912.G.4.6
Name and label corresponding parts of congruent triangles.
Corresponding Parts | Congruent Triangles
33
ID: A
106. ANS: C
The vertices naming the triangles correspond to the congruent vertices of the two triangles in the same
order.
Feedback
A
B
C
D
The letters naming the triangles correspond to the congruent vertices of the two
triangles.
Be careful with the order of the vertices.
Correct!
Are the vertices in the correct order?
PTS: 1
DIF: Average
REF: Lesson 4-3
OBJ: 4-3.2 Identify congruent transformations.
STA: MA.912.G.4.4 | MA.912.G.4.6
TOP: Identify congruent transformations.
KEY: Transformations | Congruence Transformations
107. ANS: D
The letters naming the triangles correspond to the congruent vertices of the two triangles in the same
order.
Feedback
A
B
C
D
Be careful with the order of the vertices.
Are the vertices in the correct order?
The letters naming the triangles correspond to the congruent vertices of the two
triangles.
Correct!
PTS: 1
DIF: Average
REF: Lesson 4-3
OBJ: 4-3.2 Identify congruent transformations.
STA: MA.912.G.4.4 | MA.912.G.4.6
TOP: Identify congruent transformations.
KEY: Transformations | Congruence Transformations
108. ANS: B
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the
triangles are congruent.
Feedback
A
B
C
D
Check your math.
Correct!
Use the SSS Postulate.
Does that make the angles congruent?
PTS:
OBJ:
STA:
KEY:
1
DIF: Basic
REF: Lesson 4-4
4-4.1 Use the SSS Postulate to test for triangle congruence.
MA.912.G.4.6 | MA.912.G.4.8
TOP: Use the SSS Postulate to test for triangle congruence.
SSS Postulate | Congruent Triangles
34
ID: A
109. ANS: A
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the
triangles are congruent.
Feedback
A
B
C
D
Correct!
Did you find the lengths of all the sides?
Use the SSS Postulate.
How can you tell if two triangles are congruent?
PTS: 1
DIF: Average
REF: Lesson 4-4
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
TOP: Use the SSS Postulate to test for triangle congruence.
KEY: SSS Postulate | Congruent Triangles
110. ANS: B
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the
triangles are congruent.
Feedback
A
B
C
D
Did you find the lengths of the sides?
Correct!
Do all congruent triangles have a right angle?
Use the SSS Postulate.
PTS: 1
DIF: Average
REF: Lesson 4-4
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
TOP: Use the SSS Postulate to test for triangle congruence.
KEY: SSS Postulate | Congruent Triangles
111. ANS: D
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the
triangles are congruent.
Feedback
A
B
C
D
How do you decide if two triangles are congruent?
Check your math.
Use the SSS Postulate.
Correct!
PTS:
OBJ:
STA:
KEY:
1
DIF: Average
REF: Lesson 4-4
4-4.1 Use the SSS Postulate to test for triangle congruence.
MA.912.G.4.6 | MA.912.G.4.8
TOP: Use the SSS Postulate to test for triangle congruence.
SSS Postulate | Congruent Triangles
35
ID: A
112. ANS: D
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the
triangles are congruent.
Feedback
A
B
C
D
Use the SSS Postulate.
Check your math.
How do you determine if two triangles are congruent?
Correct!
PTS: 1
DIF: Average
REF: Lesson 4-4
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
TOP: Use the SSS Postulate to test for triangle congruence.
KEY: SSS Postulate | Congruent Triangles
113. ANS: B
m∠FXA = m∠FXM + m∠AXM; ∠FXM ≅ ∠FMX
Feedback
A
B
C
D
That is the sum of which angles?
Correct!
What angle measures did you add?
That is the sum of which angles?
PTS: 1
DIF: Average
REF: Lesson 4-6
OBJ: 4-6.1 Use the properties of isosceles triangles.
TOP: Use the properties of isosceles triangles.
114. ANS: A
m∠FMR = m∠FMX + m∠XMA + m∠AMR
STA: LA.910.1.6.5 | MA.912.G.4.1
KEY: Isosceles Triangles
Feedback
A
B
C
D
Correct!
Did you subtract carefully?
What angles make up that angle?
What is the measure of ∠AMX?
PTS: 1
DIF: Average
REF: Lesson 4-6
OBJ: 4-6.1 Use the properties of isosceles triangles.
TOP: Use the properties of isosceles triangles.
36
STA: LA.910.1.6.5 | MA.912.G.4.1
KEY: Isosceles Triangles
ID: A
115. ANS: B
4y − 4 = 60
3x − 8 = 2x − 1
Feedback
A
B
C
D
Did you set the two sides equal to each other?
Correct!
How many degrees is each angle of an equilateral triangle?
How many degrees is ∠H?
PTS: 1
DIF: Basic
REF: Lesson 4-6
OBJ: 4-6.2 Use the properties of equilateral triangles.
TOP: Use the properties of equilateral triangles.
116. ANS: D
y + 12 = 30
ÊÁ ˆ˜ 2
ÁÁ UT ˜˜ + x 2 = 4 2
ÁË ˜¯
STA: LA.910.1.6.5 | MA.912.G.4.1
KEY: Equilateral Triangles
Feedback
A
B
C
D
Did you use the Pythagorean Theorem?
Did you add instead of subtract?
Check your math.
Correct!
PTS:
OBJ:
TOP:
117. ANS:
OBJ:
STA:
KEY:
118. ANS:
OBJ:
STA:
KEY:
1
DIF: Average
REF: Lesson 4-6
4-6.2 Use the properties of equilateral triangles.
Use the properties of equilateral triangles.
B
PTS: 1
DIF: Basic
4-7.1 Identify reflections, translations, and rotations.
MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
congruence transformation
B
PTS: 1
DIF: Basic
4-7.1 Identify reflections, translations, and rotations.
MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
congruence transformation
37
STA: LA.910.1.6.5 | MA.912.G.4.1
KEY: Equilateral Triangles
REF: Lesson 4-7
TOP: Congruence transformations.
REF: Lesson 4-7
TOP: Congruence transformations.
ID: A
119. ANS: B
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Look at your labels.
Correct!
Which sides are congruent?
Which sides are congruent?
PTS: 1
DIF: Basic
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
120. ANS: C
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Which leg is twice as long?
What is the hypotenuse?
Correct!
Look at your labels.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 4-8
4-8.1 Position and label triangles for use in coordinate proofs.
MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
Position and label triangles for use in coordinate proofs.
Proofs | Coordinate Proofs
38
ID: A
121. ANS: A
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Correct!
What is the base?
What is the base of that triangle?
Look at your labels.
PTS: 1
DIF: Average
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
122. ANS: D
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
What is the base?
What segment is the base?
Look at your labels.
Correct!
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 4-8
4-8.1 Position and label triangles for use in coordinate proofs.
MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
Position and label triangles for use in coordinate proofs.
Proofs | Coordinate Proofs
39
ID: A
123. ANS: D
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
What segment is the hypotenuse?
Look at your labels.
Which leg is 4a units long?
Correct!
PTS: 1
DIF: Average
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
124. ANS: C
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Is the triangle placed correctly?
Is the triangle half of an equilateral?
Correct!
What is the hypotenuse?
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 4-8
4-8.1 Position and label triangles for use in coordinate proofs.
MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
Position and label triangles for use in coordinate proofs.
Proofs | Coordinate Proofs
40
ID: A
125. ANS: B
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
What is the hypotenuse?
Correct!
Which segment is the hypotenuse?
Express the y-coordinate for point N in terms of a.
PTS: 1
DIF: Average
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
126. ANS: D
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Which segment is the base?
Where does the triangle belong?
Look at your labels.
Correct!
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 4-8
4-8.1 Position and label triangles for use in coordinate proofs.
MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
Position and label triangles for use in coordinate proofs.
Proofs | Coordinate Proofs
41
ID: A
127. ANS: A
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
Correct!
Look at your placement.
How tall is the triangle?
How tall is the triangle?
PTS: 1
DIF: Average
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
128. ANS: C
1. Use the origin as a vertex or center of the figure.
2. Place at least one side of a polygon on an axis.
3. Keep the figure within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.
Feedback
A
B
C
D
How tall is the triangle?
Look at your placement.
Correct!
How tall is the triangle?
PTS: 1
DIF: Average
REF: Lesson 4-8
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
TOP: Position and label triangles for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs
129. ANS: B
The measures of the sides opposite the angles given are compared. The longer the side, the larger its
angle.
Feedback
A
B
C
Check the sides opposite the angles.
Correct!
Check the sides opposite the angles.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 5-3
5-3.1 Recognize and apply properties of inequalities to the measures of angles of a triangle.
LA.910.1.6.5 | MA.912.G.4.7
Recognize and apply properties of inequalities to the measures of angles of a triangle.
Properties of Inequality | Triangles
42
ID: A
130. ANS: D
The sum of the lengths of any two sides must be greater than the third.
Feedback
A
B
C
D
Did you check all the sums?
Add two sides and compare to the third.
Add two sides and compare to the third.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 5-5
OBJ: 5-5.1 Apply the Triangle Inequality Theorem.
STA: LA.1112.1.6.2 | MA.912.G.4.7
TOP: Apply the Triangle Inequality Theorem.
KEY: Triangles Inequality Theorem
131. ANS: C
The sum of the lengths of any two sides must be greater than the third.
Feedback
A
B
C
D
Did you check all the sums?
Add two sides and compare to the third.
Correct!
Add two sides and compare to the third.
PTS:
OBJ:
TOP:
132. ANS:
1
DIF: Average
REF: Lesson 5-5
5-5.1 Apply the Triangle Inequality Theorem.
Apply the Triangle Inequality Theorem.
C
STA: LA.1112.1.6.2 | MA.912.G.4.7
KEY: Triangles Inequality Theorem
To find the size of each interior angle of a regular polygon, use the formula
180(n − 2)
.
n
Feedback
A
B
C
D
This is the sum of all of the interior angles, not each individual angle.
This is the value of each exterior angle.
Correct!
This is the sum of the exterior angles.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-1
6-1.1 Find the sum of the measures of the interior angles of a polygon.
MA.912.G.2.2 | MA.912.G.3.4
Find the sum of the measures of the interior angles of a polygon.
Interior Angles | Polygons
43
ID: A
133. ANS: D
To find the size of each exterior angle of a regular polygon, use the formula
360
.
n
Feedback
A
B
C
D
This is the sum of the interior angles.
This is the value of each interior angle.
This is the sum of all of the exterior angles not each individual angle.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 6-1
OBJ: 6-1.2 Find the sum of the measures of the exterior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
TOP: Find the sum of the measures of the exterior angles of a polygon.
KEY: Exterior Angles | Polygons
134. ANS: C
Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine
which segment is congruent to that segment.
Feedback
A
B
C
D
This segment is not congruent to the original segment.
Why are these segments congruent?
Correct!
Check the segment and reason.
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.1 Recognize and apply properties of the sides and angles of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Recognize and apply properties of the sides and angles of parallelograms.
KEY: Parallelograms | Properties of Parallelograms
135. ANS: D
Use the distance formula to determine the lengths of the diagonals. The distance formula is
2
d=
2
(x 1 − x 2 ) + (y 1 − y 2 ) . If the lengths are the same, then the diagonals are congruent.
Feedback
A
B
C
D
Check the lengths of both diagonals.
Check the lengths of both diagonals.
Is this the length of the entire diagonal?
Correct!
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-2
6-2.2 Recognize and apply properties of diagonals of parallelograms.
MA.912.G.3.1 | MA.912.G.3.4
Recognize and apply properties of diagonals of parallelograms.
Parallelograms | Properties of Parallelograms | Diagonals
44
ID: A
136. ANS: D
Use the distance formula to determine the lengths of the diagonals. The distance formula is
2
d=
2
(x 1 − x 2 ) + (y 1 − y 2 ) . If the lengths are the same, then the diagonals are congruent.
Feedback
A
B
C
D
Check the lengths of both diagonals.
Check the lengths of both diagonals.
Is this the length of the entire diagonal?
Correct!
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Recognize and apply properties of diagonals of parallelograms.
KEY: Parallelograms | Properties of Parallelograms | Diagonals
137. ANS: A
Using the method indicated, determine if the points form a parallelogram. If the opposite sides are
congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the
points form a parallelogram.
Feedback
A
B
C
D
Correct!
Which method was used to solve the problem?
Which method was used to solve the problem?
This is not valid reason for the quadrilateral to be a parallelogram.
PTS: 1
DIF: Average
REF: Lesson 6-3
OBJ: 6-3.2 Prove that a set of points forms a parallelogram in the coordinate plane.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
TOP: Prove that a set of points forms a parallelogram in the coordinate plane.
KEY: Parallelograms | Determining a Parallelogram
138. ANS: A
Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the
quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the
diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.
Feedback
A
B
C
D
Correct!
Are the angles congruent?
Remember to list all that apply.
Are the sides congruent?
PTS:
OBJ:
STA:
TOP:
1
DIF: Average
REF: Lesson 6-5
6-5.2 Recognize and apply the properties of squares.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
Recognize and apply the properties of squares.
KEY: Squares | Properties of Squares
45
ID: A
139. ANS: C
To find the other base, substitute the given values into the formula, median =
base 1 + base 2
.
2
Feedback
A
B
C
D
Do not add the median and base.
AB is the median not a base.
Correct!
Do not subtract the median from the base.
PTS: 1
DIF: Average
REF: Lesson 6-6
OBJ: 6-6.1 Recognize and apply the properties of trapezoids.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
TOP: Recognize and apply the properties of trapezoids.
KEY: Trapezoids | Properties of Trapezoids
140. ANS: A
To find the median, find the sum of the bases and then divide by two.
Feedback
A
B
C
D
Correct!
Do not subtract the smaller base from the larger base.
How do you find the median?
Remember to divide by two.
PTS: 1
DIF: Basic
REF: Lesson 6-6
OBJ: 6-6.2 Solve problems involving the medians of trapezoids.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
TOP: Solve problems involving the medians of trapezoids.
KEY: Trapezoids | Medians | Medians of Trapezoids
141. ANS: A
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Correct!
Are all sides the same length?
Is this a rectangle?
Rectangles have four right angles.
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-7
6-7.1 Position and label quadrilaterals for use in coordinate proofs.
Position and label quadrilaterals for use in coordinate proofs.
Proofs | Coordinate Proofs | Quadrilaterals
46
ID: A
142. ANS: B
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Are all four sides congruent?
Correct!
Is this a square?
Squares have four right angles.
PTS: 1
DIF: Basic
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
143. ANS: C
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
How many pairs of parallel sides does a trapezoid have?
Are all sides the same length?
Correct!
How many pairs of parallel sides does a trapezoid have?
PTS: 1
DIF: Average
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
144. ANS: D
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
What is the height of this figure?
Are all sides the same length?
Is this a rectangle?
Correct!
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-7
6-7.1 Position and label quadrilaterals for use in coordinate proofs.
Position and label quadrilaterals for use in coordinate proofs.
Proofs | Coordinate Proofs | Quadrilaterals
47
ID: A
145. ANS: A
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Correct!
Should all sides be congruent?
What is the height of this figure?
What is the length of each side?
PTS: 1
DIF: Average
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
146. ANS: B
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Are all sides congruent?
Correct!
What is the height of this figure?
What is the length of each side?
PTS: 1
DIF: Basic
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
147. ANS: C
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
What is the height of the figure?
Should all sides be congruent?
Correct!
What is the length of each side?
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-7
6-7.1 Position and label quadrilaterals for use in coordinate proofs.
Position and label quadrilaterals for use in coordinate proofs.
Proofs | Coordinate Proofs | Quadrilaterals
48
ID: A
148. ANS: D
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Are the sides congruent?
What is the length of each side?
What is the height of this figure?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
149. ANS: A
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
Feedback
A
B
C
D
Correct!
Is this an isosceles trapezoid?
What are the lengths of the bases?
Is this an isosceles trapezoid?
PTS: 1
DIF: Average
REF: Lesson 6-7
OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.
TOP: Position and label quadrilaterals for use in coordinate proofs.
KEY: Proofs | Coordinate Proofs | Quadrilaterals
150. ANS: C
What are the properties of the given shape? Use the properties to determine what the graph should
resemble.
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A
B
C
D
What are the lengths of the bases?
Is this an isosceles trapezoid?
Correct!
Is this an isosceles trapezoid?
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-7
6-7.1 Position and label quadrilaterals for use in coordinate proofs.
Position and label quadrilaterals for use in coordinate proofs.
Proofs | Coordinate Proofs | Quadrilaterals
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