Download First Semester (August - December) Final Review

Name: ______________________ Class: _________________ Date: _________
First Semester (August - December) Final Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Name three points that are collinear.
a. B, G, F
b. C, D, H
c.
d.
J, G, F
J, D, G
2. 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.
1
ID: A
Name: ______________________
ID: A
4. QT = 0.4 in., QV = 1.9 in.
Find the measurement of the segment.
3. PR = 18.8 mm, RS = 13.7 mm
TV = ?
a. 1.4
b. 2.3
c. 1.7
d. 1.5
PS = ?
a. 32.7 mm
b. 5.1 mm
c. 32.5 mm
d. 32.4 mm
in.
in.
in.
in.
5. Find the value of the variable and GH if H is between G and I.
GI = 5b + 1, HI = 4b − 5, HI = 7
a. b = 1.2, GH = 6.8
b. b = 1.22, GH = 7.11
c.
d.
b = 3, GH = 9
b = 3, GH = 16
Use the number line to find the measure.
6. PH
a.
b.
c.
d.
7. RK
a.
b.
c.
d.
Use the Distance Formula to find the distance
between each pair of points.
4.5
8
9
–0.5
8.
2
5
7
10
a.
50
b.
34
c. 6
d. 4
2
Name: ______________________
ID: A
⎯⎯
⎯
→
In the figure, GK bisects ∠FGH.
9.
11. If m∠FGK = 3v − 4 and m∠KGH = 2v + 7, find
x.
a.
b.
c.
d.
a.
50
b. 4
c.
34
d. 6
33
58
11
29
⎯
⎯
→
⎯⎯
→
In the figure, KJ and KL are opposite rays.
Find the coordinates of the midpoint of a
segment having the given endpoints.
⎯⎯
⎯
→
∠1 ≅ ∠2 and KM bisects ∠NKL.
10. Q ÊÁË 1, − 3 ˆ˜¯ , R ÊÁË 11, 5 ˆ˜¯
a. ÊÁË −1, 8 ˆ˜¯
b.
c.
d.
ÊÁ −10, − 8 ˆ˜
Ë
¯
ÁÊË 6, 1 ˜ˆ¯
ÊÁ −5, − 4 ˆ˜
Ë
¯
12. What bisects ∠JKN?
a. P
b.
⎯⎯
→
KP
⎯⎯
→
c. PK
d. ∠2
⎯⎯
⎯
→
13. 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.
3
Name: ______________________
ID: A
14. If m∠JKM = 5x + 18 and m∠4 = x, what is
19. The measures of two complementary angles are
m∠4?
a. 153
b. 33
c. 27
d. 12
Use the figure to find the angles.
20.
21.
22.
15. Name two acute vertical angles.
a. ∠KQL, ∠KQM
b. ∠KQL, ∠IQH
c. ∠GQI, ∠IQM
d. ∠HQL, ∠IQK
16. Name a pair of obtuse adjacent angles.
a. ∠KQG, ∠HQM
b. ∠GQL, ∠LQJ
c. ∠GQI, ∠IQM
d. ∠HQG, ∠IQH
17. Name a linear pair.
a. ∠KQG, ∠HQM
b. ∠GQL, ∠LQJ
c. ∠GQI, ∠IQM
d. ∠LQG, ∠KQM
18. Name an angle supplementary to ∠MQI.
a. ∠IQG
b. ∠GQL
c. ∠MQK
d. ∠IQH
23.
4
12q − 9 and 8q + 14. Find the measures of the
angles.
a. 42, 48
b. 4.25
c. 8.75
d. 96, 84
Two angles are supplementary. One angle
measures 26o more than the other one. Find the
measure of the two angles.
a. 77, 103
b. 32, 58
c. 167, 193
d. 76, 104
Find m∠Y if m∠Y is six more than three times
its complement.
a. 136.5
b. 43.5
c. 21
d. 69
The measure of an angle’s supplement is 24
less than twice the measure of the angle. Find
the measure of the angle and its supplement.
a. 38, 52
b. 52, 38
c. 68, 112
d. 112, 68
Rays AB and BC are perpendicular. Point D lies
in the interior of ∠ABC. If m∠ABD = 4r − 7
and m∠DBC = 8r + 1, find m∠ABD and
m∠DBC.
a. 8, 90
b. 55, 125
c. 21, 69
d. 25, 65
Name: ______________________
ID: A
26. P = 49 units. Find the length of each side.
Find the length of each side of the polygon for
the given perimeter.
24. P = 48 cm
a.
b.
c.
d.
8 cm
6 cm
4 cm
3 cm
25. P = 60 in. Find the length of each side.
a.
b.
c.
d.
a.
b.
c.
d.
11
10
12
10
in.,
in.,
in.,
in.,
18 units, 18
18.66 units,
27 units, 27
26 units, 26
units, 13 units
18.66 units, 13.66 units
units, 22 units
units, 21 units
Make a conjecture about the next item in the
sequence.
27. 1, 4, 16, 64, 256
a. 1024
b. 1025
c. 4096
d. 1022
28. 6, 8, − 32, − 30, 120
a. 122
b. −480
c. −488
d. 116
20 in., 35 in.
18.5 in., 31.5 in.
21.5 in., 38.5 in.
15 in., 35 in.
Determine whether the conjecture is true or
false. Give a counterexample for any false
conjecture.
29. 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.
5
Name: ______________________
ID: A
30. Given: point B is in the interior of ∠ADC.
32. Given: ∠ABC, ∠DBE are coplanar.
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.
31. 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.
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.
33. 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.
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false,
find a counterexample.
34. 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
In the figure below, points A, B, C, and F lie on plane
statement is true.
P . State the postulate that can be used to show each
35. 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.
6
Name: ______________________
ID: A
36. 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.
←⎯
⎯
→
←⎯
⎯
→
40. In the figure, m∠RPZ = 95 and TU Ä RQ Ä VW.
Find the measure of angle WSP.
a.
b.
c.
d.
85
75
95
65
41. In the figure, AB Ä CD. Find x and y.
37. Name all planes intersecting plane CDI.
a. ABC, CBG, ADI, FGH
b. CBA, DAF, HGF
c. BAD, GFI, CBG, GFA
d. DAB, CBG, FAD
38. Name all segments parallel to GF.
a. BC, AD, HI
b. AB, CD, HI
c. CD, HI
d. AB, CD
39. Name all segments skew to BC.
a. FI, AD, FA, DI
b. FG, GH, HI, FI
c. CD, AB, BG, CH
d. GF, HI, DI, AF
a.
b.
c.
d.
7
x = 32, y = 140
x = 140, y = 52
x = 52, y = 140
x = 38, y = 154
Name: ______________________
ID: A
42. In the figure, p Ä q. Find m∠1.
Determine the slope of the line that contains the
given points.
43. T ÊÁË 6, 3 ˆ˜¯ , V ÊÁË 8, 8 ˆ˜¯
a. 5/2
b. -2/5
c. 2/5
d. 0
a.
b.
c.
d.
m∠1
m∠1
m∠1
m∠1
= 61
= 35
= 55
= 64
←⎯
⎯
→
←⎯
→
Determine whether WX and YZ are parallel, perpendicular, or neither.
44. 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
8
Name: ______________________
ID: A
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem
that justifies your answer.
45. ∠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
Find the measures of the sides of ΔABC and classify the triangle by its sides.
46. A ÁÊË 5, − 2 ˜ˆ¯ , B ÁÊË 7, 2 ˜ˆ¯ , C ÁÊË 3, 5 ˜ˆ¯
a. equilateral
b. isosceles
c.
d.
scalene
obtuse
c.
d.
m∠1 = 47, m∠2 = 74, m∠3 = 69
m∠1 = 47, m∠2 = 59, m∠3 = 64
Find each measure.
47. m∠1, m∠2, m∠3
a. m∠1 = 64, m∠2 = 74, m∠3 = 52
b. m∠1 = 64, m∠2 = 47, m∠3 = 52
9
Name: ______________________
ID: A
48. m∠1, m∠2, m∠3
a. m∠1 = 77, m∠2 = 41, m∠3 = 37
b. m∠1 = 77, m∠2 = 36, m∠3 = 30
c.
d.
m∠1 = 82, m∠2 = 41, m∠3 = 37
m∠1 = 82, m∠2 = 92, m∠3 = 30
c.
d.
m∠1 = 51, m∠2 = 101, m∠3 = 101
m∠1 = 74, m∠2 = 152, m∠3 = 74
49. m∠1, m∠2, m∠3
a. m∠1 = 74, m∠2 = 129, m∠3 = 101
b. m∠1 = 46, m∠2 = 129, m∠3 = 129
Refer to the figure. ΔARM, ΔMAX, and ΔXFM
are all isosceles triangles.
52. What is m∠MAX?
a. 16
b. 38
c. 36
d. 108
53. What is m∠RAX?
a. 74
b. 68
c. 64
d. 78
50. What is m∠RAM?
a. 23
b. 38
c. 42
d. 35
51. What is m∠AMX?
a. 80
b. 38
c. 64
d. 72
10
Name: ______________________
ID: A
54. Triangle FJH is an equilateral triangle. Find x
56. Triangle RSU is an equilateral triangle. RT
and y.
a.
b.
c.
d.
x=
bisects US. Find x and y.
7
5
, y = 16
a. x = − 13 , y = 32
x = 7, y = 16
x=
7
5
b. x = 12 , y = 62
, y = 14
c. x = 13 , y = 62
x = 7, y = 14
d. x = 12 , y = 32
55. Triangles ABC and AFD are vertical congruent
equilateral triangles. Find x and y.
57. Triangle RSU is an equilateral triangle. RT
bisects US. Find x and y.
a. x = 7, y = 27
b. x = 73 , y = 27
c. x = 73 , y = 28
d. x = 7, y = 33
a.
b.
c.
d.
x=4
5, y=9
x=4
3 , y = 21
x=4
5 , y = 21
x=4
3, y=9
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
58. 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.
11
Name: ______________________
ID: A
59. An isosceles triangle has a base 9.6 units long.
Identify the similar triangles. Find x.
If the congruent side lengths have measures to
the first decimal place, what is the shortest
possible length of the sides?
a. 4.9
b. 19.3
c. 4.7
d. 9.7
61.
Solve each proportion.
60. x + 1 = 14
x−1
20
a. -3/17
b. 10/7
c. 7/10
d. -17/3
a.
b.
c.
d.
12
ΔABC ∼ ΔEDF; x = 12
ΔABC ∼ ΔEDF; x = 3
ΔABC ∼ ΔEDF; x = 4
ΔABC ∼ ΔDEF; x = 3
Name: ______________________
ID: A
64.
Determine whether each pair of triangles is
similar. Justify your answer.
62.
a.
b.
c.
d.
yes; ΔEDF ∼ ΔBCA by AA Similarity
yes; ΔEDF ∼ ΔABC by AA Similarity
yes; ΔEDF ∼ ΔBCA by ASA Similarity
No; there is not enough information to
determine similarity.
Find x and the measures of the indicated parts.
65.
a.
b.
c.
d.
No; sides are not proportional.
yes; ΔEDF ∼ ΔBAC by SSS Similarity
yes; ΔEDF ∼ ΔBCA by SSS Similarity
yes; ΔEDF ∼ ΔABC by SSS Similarity
a.
b.
c.
d.
No; the sides are not congruent.
yes; ΔEDF ∼ ΔBCA by SSS Similarity
yes; ΔEDF ∼ ΔBCA by ASA Similarity
yes; ΔEDF ∼ ΔBCA by SAS Similarity
AB and BC
a. x = 5, AB = 14, BC = 8
b. x = −1.6, AB = 0.8, BC = 1.4
c. x = 5, AB = 6, BC = 2
d. x = −1.6, AB = 7.2, BC = 4.6
63.
66.
AB
a. x = 7, AB = 20
b. x = 7, AB = 16
c.
d.
x = 7, AB = 36
x = 7, AB = 4
13
Name: ______________________
ID: A
67.
AB
a. x = 32 , AB = 6
c.
x=
14
3
, AB =
28
3
b. x = 32 , AB = 3
d.
x=
14
3
, AB = 28
x=
3
7
68.
BD = 4x
CE = 2x + 2
BD and CE
a. x = 5, BD = 20, CE = 12
b. x = 5, BD = 20, CE = 8
c.
d.
, BD =
12
7
, CE =
20
7
x = 3, BD = 12, CE = 20
69. Count the number of dots in each arrangement. How many dots will be in the sixth triangular number?
a. 6
b. 15
c.
d.
21
28
14
Name: ______________________
ID: A
Short Answer
Determine whether each pair of triangles is
similar. Justify your answer.
70.
71.
15
ID: A
First Semester (August - December) Final Review
Answer Section
MULTIPLE CHOICE
1. ANS: A
Collinear points are points on the same line.
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:
NAT:
KEY:
2. ANS:
1
DIF:
NCTM GM.2
Collinear Points
D
Average
OBJ: 1-1.2 Identify collinear points.
STA: 1.0
TOP: Identify collinear points.
Points that lie on the same plane are said to be coplanar. Three points are always coplanar but if the fourth
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:
OBJ:
NAT:
TOP:
KEY:
3. ANS:
1
DIF: Average
1-1.3 Identify coplanar points and intersecting lines in space.
NCTM GM.2
STA: 1.0
Identify coplanar points and intersecting lines in space.
Coplanar Points | Intersecting Lines | Lines in Space
C
PS has the same length as PR and RS combined.
Feedback
A
B
C
D
Did you add correctly?
PS contains both PR and RS.
Correct!
Try adding that again.
PTS: 1
DIF: Basic
NAT: NCTM ME.2 | NCTM ME.2a
KEY: Measurement | Line Segments
OBJ: 1-2.1 Measure segments.
TOP: Measure segments.
1
ID: A
4. ANS: D
TV is the length of QV minus the length of QT.
Feedback
A
B
C
D
Try subtracting that again.
You need to subtract, not add.
Try subtracting that again.
Correct!
PTS:
NAT:
KEY:
5. ANS:
1
DIF: Basic
NCTM ME.2 | NCTM ME.2a
Measurement | Line Segments
C
OBJ: 1-2.1 Measure segments.
TOP: Measure segments.
Solve for b first using HI’s two values. GI = GH + HI. Solve for GH.
Feedback
A
B
C
D
Which two segments in the question are the same?
Which two segments in the question are the same?
Correct!
Which segment are you solving for?
PTS:
NAT:
KEY:
6. ANS:
1
DIF: Average
NCTM NO.1
Measurement | Compute Measures
C
OBJ: 1-2.3 Compute with measures.
TOP: Compute with measures.
The distance between two points a and b is |b − a | or |a − b |.
Feedback
A
B
C
D
You are looking for the measure, not the half measure.
Add those numbers again.
Correct!
You are looking for the measure, not the midpoint.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
1-3.1 Find the distance between two points on a number line.
NCTM GM.2 | NCTM GM.2a
Find the distance between two points on a number line.
Distance | Number Lines | Distance Between Two Points
2
ID: A
7. ANS: D
The distance between two points a and b is |b − a | or |a − b |.
Feedback
A
B
C
D
You are looking for the measure, not the midpoint.
You are looking for the measure, not the half measure.
Add those numbers again.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
8. ANS:
1
DIF: Average
1-3.1 Find the distance between two points on a number line.
NCTM GM.2 | NCTM GM.2a
Find the distance between two points on a number line.
Distance | Number Lines | Distance Between Two Points
B
The Distance Formula is d =
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2 .
ÁË 2
ÁË 2
1˜
1˜
¯
¯
Feedback
A
B
C
D
With distance you subtract the coordinates.
Correct!
Be a little more precise.
Did you use the distance formula correctly?
PTS:
OBJ:
NAT:
TOP:
KEY:
9. ANS:
1
DIF: Basic
1-3.2 Find the distance between two points on a coordinate plane.
NCTM GM.2 | NCTM GM.2a
Find the distance between two points on a coordinate plane.
Distance | Coordinate Plane | Distance Between Two Points
C
The Distance Formula is d =
2
2
ÁÊÁ x − x ˜ˆ˜ + ÁÊÁ y − y ˜ˆ˜ .
1¯
1¯
Ë 2
Ë 2
Feedback
A
B
C
D
With distance you subtract the coordinates.
Did you use the distance formula correctly?
Correct!
Be a little more precise.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Basic
1-3.2 Find the distance between two points on a coordinate plane.
NCTM GM.2 | NCTM GM.2a
Find the distance between two points on a coordinate plane.
Distance | Coordinate Plane | Distance Between Two Points
3
ID: A
10. ANS: C
ÊÁ Ê
ÁÁ ÁÁ x + x ˜ˆ˜
ÁË 1
2¯
Ê
ˆ
Ê
ˆ
Á
˜
Á
˜
The formula for the midpoint between two points ÁË x 1 , y 1 ˜¯ , ÁË x 2 , y 2 ˜¯ is ÁÁÁÁ
ÁÁ
2
ÁÁ
Ë
ÁÊÁ y + y ˜ˆ˜
2¯
Ë 1
,
2
ˆ˜
˜˜
˜˜
˜˜ .
˜˜
˜˜
˜¯
Feedback
A
B
C
D
Did you use the midpoint formula?
Did you use the midpoint formula correctly?
Correct!
Do you subtract then divide by two?
PTS:
NAT:
KEY:
11. ANS:
1
DIF: Average
NCTM ME.1
Midpoint | Line Segment
D
OBJ: 1-3.3 Find the midpoint of a segment.
TOP: Find the midpoint of a segment.
⎯⎯
⎯
→
Since GK bisects ∠FGH, x = y and 3v − 4 = 2v + 7. Solve for v, then substitute into either side of the
equation to find x.
Feedback
A
B
C
D
Don’t forget to subtract.
You are not finding the measure of FGH. You are finding x.
You are not finding v. You are finding x.
Correct!
PTS:
NAT:
KEY:
12. ANS:
1
DIF: Basic
OBJ: 1-4.3 Identify and use congruent angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use congruent angles.
Angles | Congruent Angles | Congruency
B
⎯⎯
→
A ray bisects an angle. K is the endpoint of that ray, not P. The answer is KP .
Feedback
A
B
C
D
Is a bisector a point?
Correct!
Is P the endpoint of that ray?
Is a bisector an angle?
PTS: 1
DIF: Basic
NAT: NCTM GM.1 | NCTM GM.1a
KEY: Angle Bisectors
OBJ: 1-4.4 Identify and use the bisector of an angle.
TOP: Identify and use the bisector of an angle.
4
ID: A
13. ANS: A
∠MKH > 90 so it is obtuse.
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:
NAT:
KEY:
14. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1a
Angle Bisectors
C
OBJ: 1-4.4 Identify and use the bisector of an angle.
TOP: Identify and use the bisector of an angle.
m∠JKM + m∠4 = 180
5x + 18 + x = 180
6x = 180 − 18
x = 27
Feedback
A
B
C
D
That is the measure of angle JKM.
You forgot to add in x.
Correct!
Opposite rays add up to 180.
PTS:
NAT:
KEY:
15. ANS:
1
DIF: Average
NCTM GM.1 | NCTM GM.1a
Angle Bisectors
B
OBJ: 1-4.4 Identify and use the bisector of an angle.
TOP: Identify and use the bisector of an angle.
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
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
5
ID: A
16. 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:
NAT:
KEY:
17. ANS:
1
DIF: Basic
OBJ: 1-5.1 Identify and use special pairs of angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
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:
NAT:
KEY:
18. ANS:
1
DIF: Average
OBJ: 1-5.1 Identify and use special pairs of angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
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
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
6
ID: A
19. ANS: A
Complementary angles are two angles whose measures have a sum of 90.
Feedback
A
B
C
D
Correct!
Is that the value of q, or the measure of the angles?
What is the definition of complementary?
Is the sum of those angles 90 degrees?
PTS:
NAT:
KEY:
20. ANS:
1
DIF: Average
OBJ: 1-5.1 Identify and use special pairs of angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
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 the sum of those two measures?
Is the measure of one angle 26 more than the other?
PTS:
NAT:
KEY:
21. ANS:
1
DIF: Average
OBJ: 1-5.1 Identify and use special pairs of angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
D
Complementary angles are two angles whose measures have a sum of 90.
Feedback
A
B
C
D
Did you write and solve an equation?
What is the definition of complementary?
You are looking for its complement.
Correct!
PTS: 1
DIF: Average
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
7
ID: A
22. ANS: C
Supplementary angles are two angles whose measures have a sum of 180.
Feedback
A
B
C
D
What is the definition of supplementary?
What is the definition of complementary?
Correct!
You want the angle first, then its supplement.
PTS:
NAT:
KEY:
23. ANS:
1
DIF: Average
OBJ: 1-5.1 Identify and use special pairs of angles.
NCTM GM.1 | NCTM GM.1a
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
D
Lines that form right angles are perpendicular. A right angle measures 90.
Feedback
A
B
C
D
Substitute back into the angles.
What is the measure of the angle created by perpendicular rays?
What is the value of r?
Correct!
PTS:
NAT:
KEY:
24. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1a
Perpendicular Lines
B
OBJ: 1-5.2 Identify perpendicular lines.
TOP: Identify perpendicular lines.
In the case of a regular figure, the length of each side is the perimeter divided by the number of sides.
Feedback
A
B
C
D
Is the figure a hexagon?
Correct!
Is the figure a dodecagon?
How many sides are there?
PTS: 1
DIF: Basic
OBJ: 1-6.3 Find the perimeters of polygons.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
TOP: Find the perimeters of polygons.
KEY: Perimeter | Polygons
8
ID: A
25. ANS: B
Perimeter is the sum of the sides.
Feedback
A
B
C
D
What is the sum of the sides?
Correct!
Did you find the value of y?
What is the value of y?
PTS:
NAT:
TOP:
26. ANS:
1
DIF: Average
OBJ: 1-6.3 Find the perimeters of polygons.
NCTM PS.1 | NCTM PS.2 | NCTM PS.3
Find the perimeters of polygons.
KEY: Perimeter | Polygons
A
Perimeter is the sum of the sides.
Feedback
A
B
C
D
Correct!
Check your math.
Did you add all three sides?
What is the sum of the three sides?
PTS:
NAT:
TOP:
27. ANS:
1
DIF: Average
OBJ: 1-6.3 Find the perimeters of polygons.
NCTM PS.1 | NCTM PS.2 | NCTM PS.3
Find the perimeters of polygons.
KEY: Perimeter | Polygons
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:
OBJ:
STA:
KEY:
1
DIF: Basic
2-1.1 Make conjectures based on inductive reasoning.
NAT: NCTM RP.2
1.0
TOP: Make conjectures based on inductive reasoning.
Inductive Reasoning | Conjectures
9
ID: A
28. ANS: A
Start with 6. Do one operation to get the next number. Do a different operation to get the next number.
Repeat.
Feedback
A
B
C
D
Correct!
What operation should come next?
What operations are involved?
Check your math.
PTS:
OBJ:
STA:
KEY:
29. ANS:
1
DIF: Average
2-1.1 Make conjectures based on inductive reasoning.
NAT: NCTM RP.2
1.0
TOP: Make conjectures based on inductive reasoning.
Inductive Reasoning | Conjectures
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:
NAT:
KEY:
30. ANS:
1
DIF:
NCTM RP.3
Counterexamples
C
Basic
OBJ: 2-1.2 Find counterexamples.
STA: 1.0 | 3.0
TOP: Find counterexamples.
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:
NAT: NCTM RP.3
KEY: Counterexamples
Basic
OBJ: 2-1.2 Find counterexamples.
STA: 1.0 | 3.0
TOP: Find counterexamples.
10
ID: A
31. 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:
NAT:
KEY:
32. ANS:
1
DIF:
NCTM RP.3
Counterexamples
C
Basic
OBJ: 2-1.2 Find counterexamples.
STA: 1.0 | 3.0
TOP: Find counterexamples.
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:
NAT:
KEY:
33. ANS:
1
DIF:
NCTM RP.3
Counterexamples
B
Basic
OBJ: 2-1.2 Find counterexamples.
STA: 1.0 | 3.0
TOP: Find counterexamples.
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:
NAT: NCTM RP.3
KEY: Counterexamples
Basic
OBJ: 2-1.2 Find counterexamples.
STA: 1.0 | 3.0
TOP: Find counterexamples.
11
ID: A
34. ANS: C
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
Check the statement again.
Check the statement again.
Correct!
What is the definition of converse?
PTS:
NAT:
TOP:
35. ANS:
1
DIF: Basic
OBJ: 2-3.2 Write the converse of if-then statements.
NCTM RP.3
STA: 3.0
Write the converse of if-then statements.
KEY: Converse | If-Then Statements
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:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
2-5.1 Identify and use basic postulates about points, lines, and planes.
NCTM RP.1
STA: 1.0 | 2.0
Identify and use basic postulates about points, lines, and planes.
Points | Lines | Planes
12
ID: A
36. 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:
NAT:
TOP:
KEY:
37. ANS:
1
DIF: Average
2-5.1 Identify and use basic postulates about points, lines, and planes.
NCTM RP.1
STA: 1.0 | 2.0
Identify and use basic postulates about points, lines, and planes.
Points | Lines | Planes
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 CDI in a line?
This plane has four lines to intersect with other planes.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Basic
3-1.1 Identify the relationships between two lines or two planes.
NCTM GM.1 | NCTM GM.1a
STA: 1.0
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
13
ID: A
38. ANS: B
Coplanar segments that do not intersect are parallel.
Feedback
A
B
C
D
Are those parallel to GF?
Correct!
Is that all?
Is that all?
PTS:
OBJ:
NAT:
TOP:
KEY:
39. ANS:
1
DIF: Basic
3-1.1 Identify the relationships between two lines or two planes.
NCTM GM.1 | NCTM GM.1a
STA: 1.0
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
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 segment BC?
Skew lines are not coplanar.
Do any of those segments intersect segment BC?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
40. ANS:
1
DIF: Average
3-1.1 Identify the relationships between two lines or two planes.
NCTM GM.1 | NCTM GM.1a
STA: 1.0
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
A
Corresponding angles are congruent.
Alternate interior angles are congruent.
Consecutive interior angles are supplementary.
Alternate exterior angles are congruent.
Feedback
A
B
C
D
Correct!
What is the sum of supplementary angles?
Are those angles congruent or supplementary?
What do supplementary angles add up to?
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
3-2.1 Use the properties of parallel lines to determine congruent angles.
NCTM AL.2c | NCTM ME.1
STA: 2.0 | 7.0
Use the properties of parallel lines to determine congruent angles.
Parallel Lines | Congruent Angles
14
ID: A
41. ANS: C
Corresponding angles are congruent.
Alternate interior angles are congruent.
Consecutive interior angles are supplementary.
Alternate exterior angles are congruent.
Feedback
A
B
C
D
What do supplementary angles add up to?
What do the angles of a right triangle add up to?
Correct!
Is that triangle isosceles?
PTS:
NAT:
TOP:
42. ANS:
1
DIF: Average
OBJ: 3-2.2 Use algebra to find angle measures.
NCTM AL.4a | NCTM GM.2 | NCTM GM.2a
Use algebra to find angle measures. KEY: Angles | Angle Measures
D
Extend v to intersect with p. This creates a linear pair at point S with angles measuring 119° (given) and
61°. The angles formed by the intersection of v and p (also linear pairs) measure 125° (corresponding
angles) and 55° with the latter being one of the interior angles of the triangle formed by t, p and v. Since the
sum of the angles of a triangle is 180°, the angle that is vertical to <1 is 64°, thus making <1 64° as well.
Feedback
A
B
C
D
Extend v as a transversal of q and p.
Extend v as a transversal of q and p.
Extend v as a transversal of q and p.
Correct!
PTS:
NAT:
TOP:
43. ANS:
1
DIF: Average
OBJ: 3-2.2 Use algebra to find angle measures.
NCTM AL.4a | NCTM GM.2 | NCTM GM.2a
Use algebra to find angle measures. KEY: Angles | Angle Measures
A
ÊÁ y − y ˆ˜
ÁË 2
1˜
¯
The formula for slope is Ê
.
ÁÁ x − x ˆ˜˜
1¯
Ë 2
Feedback
A
B
C
D
Correct!
You are not solving for the slope of the perpendicular.
Remember y over x.
Subtract y from y and x from x.
PTS: 1
DIF: Basic
OBJ: 3-3.1 Find slopes of lines.
NAT: NCTM GM.1b | NCTM GM.2 | NCTM GM.2a
TOP: Find slopes of lines.
KEY: Slope | Slope of Lines
15
ID: A
44. 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:
OBJ:
NAT:
TOP:
KEY:
45. ANS:
1
DIF: Average
3-3.2 Use slope to identify parallel lines and perpendicular lines.
NCTM AL.2 | NCTM AL.2c | NCTM RE.2
Use slope to identify parallel lines and perpendicular lines.
Parallel Lines | Perpendicular Lines | Slope
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 2 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:
NAT:
TOP:
1
DIF: Basic
3-5.1 Recognize angle conditions that occur with parallel lines.
NCTM GM.1b | NCTM GM.1c | NCTM RP.3
STA: 7.0 | 16.0
Recognize angle conditions that occur with parallel lines.
KEY: Angles | Parallel Lines
16
ID: A
46. ANS: C
Use the Distance Formula to find the lengths of the sides.
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2
ÁË 2
ÁË 2
1˜
1˜
¯
¯
If AB = BC or BC = CA or AB = CA, then the triangle is isosceles.
If AB = BC = CA, then the triangle is equilateral.
If neither of the above, the triangle is scalene.
d=
Feedback
A
B
C
D
Use the distance formula to find the lengths of the sides.
Did you use the distance formula?
Correct!
What are the lengths of the sides?
PTS:
NAT:
TOP:
47. ANS:
1
DIF: Average
OBJ: 4-1.2 Identify and classify triangles by sides.
NCTM GM.1 | NCTM GM.1b
STA: 12.0
Identify and classify triangles by sides.
KEY: Triangles | Classify Triangles
C
The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.
Feedback
A
B
C
D
What do you know about vertical angles?
What do you know about vertical angles?
Correct!
Use the Angle Sum Theorem.
PTS:
NAT:
TOP:
48. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1b
Apply the Angle Sum Theorem.
B
OBJ: 4-2.1 Apply the Angle Sum Theorem.
STA: 2.0 | 12.0
KEY: Angle Sum Theorem
The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.
Feedback
A
B
C
D
Did you use the Angle Sum Theorem.
Correct!
Use the Angle Sum Theorem.
Use the Angle Sum Theorem.
PTS: 1
DIF: Average
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Apply the Angle Sum Theorem.
OBJ: 4-2.1 Apply the Angle Sum Theorem.
STA: 2.0 | 12.0
KEY: Angle Sum Theorem
17
ID: A
49. ANS: A
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
Correct!
What is the sum of the measures of the angles in a triangle?
Did you use the Exterior Angle Theorem?
Use the Exterior Angle Theorem.
PTS:
NAT:
TOP:
50. ANS:
1
DIF: Average
OBJ: 4-2.2 Apply the Exterior Angle Theorem.
NCTM GM.1 | NCTM GM.1b
STA: 2.0 | 12.0 | 13.0
Apply the Exterior Angle Theorem. KEY: Exterior Angle Theorem
B
Since ΔARM is isosceles, ∠RAM ≅ ∠RMA.
Feedback
A
B
C
D
Remember the definition of isosceles.
Correct!
Is that the base angle of an isosceles triangle?
Remember the definition of isosceles.
PTS:
NAT:
TOP:
51. ANS:
1
DIF: Basic
OBJ: 4-6.1 Use properties of isosceles triangles.
NCTM GM.1 | NCTM GM.1a
STA: 2.0 | 4.0 | 5.0
Use properties of isosceles triangles.
KEY: Isosceles Triangles
D
Since ΔMAX is isosceles, ∠AXM ≅ ∠AMX.
Feedback
A
B
C
D
Is that the base angle of an isosceles triangle?
Remember the definition of isosceles.
What do you know about base angles of an isosceles triangle?
Correct!
PTS: 1
DIF: Basic
OBJ: 4-6.1 Use properties of isosceles triangles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 2.0 | 4.0 | 5.0
TOP: Use properties of isosceles triangles.
KEY: Isosceles Triangles
18
ID: A
52. ANS: C
Since ΔMAX is isosceles, ∠AXM ≅ ∠AMX. Subtract those from 180 to get the answer.
Feedback
A
B
C
D
How many degrees in a triangle?
Is that the vertex angle?
Correct!
Subtract both base angles from 180.
PTS:
NAT:
TOP:
53. ANS:
1
DIF: Average
OBJ: 4-6.1 Use properties of isosceles triangles.
NCTM GM.1 | NCTM GM.1a
STA: 2.0 | 4.0 | 5.0
Use properties of isosceles triangles.
KEY: Isosceles Triangles
A
Add m∠MAX and m∠RAM.
Feedback
A
B
C
D
Correct!
That is the sum of which angles?
Did you add carefully?
That is the sum of which angles?
PTS:
NAT:
TOP:
54. ANS:
1
DIF: Average
OBJ: 4-6.1 Use properties of isosceles triangles.
NCTM GM.1 | NCTM GM.1a
STA: 2.0 | 4.0 | 5.0
Use properties of isosceles triangles.
KEY: Isosceles Triangles
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 angle H?
PTS: 1
DIF: Basic
OBJ: 4-6.2 Use properties of equilateral triangles.
NAT: NCTM GM.2 | NCTM GM.2a
STA: 2.0 | 4.0 | 5.0
TOP: Use properties of equilateral triangles.
KEY: Equilateral Triangles
19
ID: A
55. ANS: A
(2y + 6) + (2y + 6) + (2y + 6) = 180
x + 4 = 2x − 3
Feedback
A
B
C
D
Correct!
What do you know about the sides of an equilateral triangle?
How many degrees is each angle of an equilateral triangle?
Did you add or subtract when solving for y?
PTS:
NAT:
TOP:
56. ANS:
1
DIF: Average
OBJ: 4-6.2 Use properties of equilateral triangles.
NCTM GM.2 | NCTM GM.2a
STA: 2.0 | 4.0 | 5.0
Use properties of equilateral triangles.
KEY: Equilateral Triangles
D
y − 2 = 30
8x + 1 = 2(5x)
Feedback
A
B
C
D
Can x be negative?
What is the measure of angle TRS?
Check your math.
Correct!
PTS:
NAT:
TOP:
57. ANS:
1
DIF: Average
OBJ: 4-6.2 Use properties of equilateral triangles.
NCTM GM.2 | NCTM GM.2a
STA: 2.0 | 4.0 | 5.0
Use properties of equilateral triangles.
KEY: Equilateral Triangles
D
2y + 12 = 30
Ê
ˆ2
2
2
4 + x = ÁÁÁÁ RU ˜˜˜˜
Ë
¯
Feedback
A
B
C
D
Did you use the Pythagorean Theorem correctly?
Check your math.
Should you have subtracted?
Correct!
PTS: 1
DIF: Average
OBJ: 4-6.2 Use properties of equilateral triangles.
NAT: NCTM GM.2 | NCTM GM.2a
STA: 2.0 | 4.0 | 5.0
TOP: Use properties of equilateral triangles.
KEY: Equilateral Triangles
20
ID: A
58. 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:
NAT:
TOP:
59. ANS:
1
DIF: Basic
OBJ: 5-4.1 Apply the Triangle Inequality Theorem.
NCTM GM.2 | NCTM GM.2a
STA: 6.0 | 12.0 | 13.0
Apply the Triangle Inequality Theorem.
KEY: Triangles Inequality Theorem
A
The sum of the lengths of any two sides must be greater than the third.
Feedback
A
B
C
D
Correct!
Would both sides have to be longer than the base?
Is the sum of the two sides longer than the base?
Is that the shortest possible length?
PTS:
OBJ:
NAT:
TOP:
KEY:
60. ANS:
1
DIF: Average
5-4.2 Determine the shortest distance between a point and a line.
NCTM AL.2 | NCTM AL.2b | NCTM GM.1
STA: 6.0 | 12.0 | 13.0
Determine the shortest distance between a point and a line.
Distance | Distance Between a Point and a Line
D
Find the cross products. Multiply. Divide each side by the coefficient of the variable.
Feedback
A
B
C
D
Reverse the numerator and denominator.
Check your cross multiplication.
The left side of the proportion cannot be reduced before cross multiplying.
Correct!
PTS: 1
DIF: Average
NAT: NCTM GM.1 | NCTM GM.1b
KEY: Proportions
OBJ: 6-1.2 Use properties of proportions.
TOP: Use properties of proportions.
21
ID: A
61. ANS: B
10
1
=
40
4
1
x
=
4
12
12 = 4x
12
4x
=
4
4
3=x
Feedback
A
B
C
D
Is AC the same length as EF?
Correct!
Check the ratio of the corresponding sides.
Check the similarity statement.
PTS:
NAT:
TOP:
62. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1b
Identify similar triangles.
C
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional. The ratio of the corresponding sides is 1:3.
Feedback
A
B
C
D
Are the sides proportional?
Check the similarity statement.
Correct!
Check the similarity statement.
PTS: 1
DIF: Basic
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Identify similar triangles.
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
22
ID: A
63. ANS: D
EF ≅ RS
DF ≅ RT
∠F ≅ ∠S
so ΔEDF ∼ ΔBCA.
Feedback
A
B
C
D
The triangles are similar.
Are all the sides labeled?
Is there an ASA Similarity?
Correct!
PTS:
NAT:
TOP:
64. ANS:
1
DIF: Average
NCTM GM.1 | NCTM GM.1b
Identify similar triangles.
A
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
∠A ≅ ∠F
∠B ≅ ∠E
so ΔEDF ∼ ΔBCA.
Feedback
A
B
C
D
Correct!
Check the similarity statement.
Is there an ASA similarity?
The triangles are similar.
PTS:
NAT:
TOP:
65. ANS:
1
DIF: Average
NCTM GM.1 | NCTM GM.1b
Identify similar triangles.
A
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Check your ratio.
What are the values of AB and BC?
Check your addition.
PTS:
NAT:
TOP:
KEY:
1
DIF: Average
OBJ: 6-3.2 Use similar triangles to solve problems.
NCTM GM.1 | NCTM GM.1b
STA: 4.0 | 5.0 | 12.0
Use similar triangles to solve problems.
Similar Triangles | Solve Problems
23
ID: A
66. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Which side is AB?
Check your operations.
Which side does the question ask you to find?
PTS:
NAT:
TOP:
KEY:
67. ANS:
1
DIF: Average
OBJ: 6-3.2 Use similar triangles to solve problems.
NCTM GM.1 | NCTM GM.1b
STA: 4.0 | 5.0 | 12.0
Use similar triangles to solve problems.
Similar Triangles | Solve Problems
B
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Check your multiplication.
Correct!
Check your ratio.
Check your multiplication.
PTS:
NAT:
TOP:
KEY:
68. ANS:
1
DIF: Average
OBJ: 6-3.2 Use similar triangles to solve problems.
NCTM GM.1 | NCTM GM.1b
STA: 4.0 | 5.0 | 12.0
Use similar triangles to solve problems.
Similar Triangles | Solve Problems
A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Check your addition.
Check the ratios.
Check the ratios and your multiplication.
PTS:
NAT:
TOP:
KEY:
1
DIF: Average
OBJ: 6-3.2 Use similar triangles to solve problems.
NCTM GM.1 | NCTM GM.1b
STA: 4.0 | 5.0 | 12.0
Use similar triangles to solve problems.
Similar Triangles | Solve Problems
24
ID: A
69. ANS: C
In the sixth triangular number, the bottom row will contain six dots. The row above the bottom row will
contain five dots. This continues until the top row contains one dot. The total number of dots is 21.
Feedback
A
B
C
D
This is the arrangement number not the number of dots in the arrangement.
This is the number of dots in the fifth arrangement.
Correct!
This is the number of dots in the seventh arrangement.
PTS: 1
DIF: Basic
OBJ: 6-6.1 Recognize and describe characteristics of fractals.
TOP: Recognize and describe characteristics of fractals.
KEY: Fractals
SHORT ANSWER
70. ANS:
yes; ΔABC ∼ ΔDEF by SSS Similarity.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
PTS: 1
DIF: Average
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Identify similar triangles.
71. ANS:
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
yes; ΔUYW ∼ ΔVXW by AA Similarity.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
PTS: 1
DIF: Average
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Identify similar triangles.
OBJ: 6-3.1 Identify similar triangles.
STA: 4.0 | 5.0 | 12.0
KEY: Similar Triangles
25