Download Geometry 1st Semester Test * Ch

Geometry
1st Semester review
Name__________________
1. What are the next three numbers in this sequence? 0, 3, 9, 18, …
j
For Exercises 2 – 4, refer to the figure to the right. 
k
Q
R
2. Name the point(s) collinear to points H and I.
H
L
G
n
I
M
O
3. Name all the point(s) coplanar to line j.
N
F
m
J
K
P
4. Name three noncollinear points.
S
5. Find DF if DE = 23, EF = 48, and E is between D and F.
For Exercises 6 – 7, refer to the given information and the figure below.
6. Find the length of CE .
A
B
D
C
A
7. Find the length of BD .
B
C
D
E
Given: AE = 30, AB = 5, AB = BC, CD = DE
8. Point Y is between X and Z. Find the length of XY if XY = 5x + 2,
YZ= 7x + 8, and XZ = 70.
9. Use points M(4, 2), N(4, 7), P(-1, 3) and Q(5, -2) to find each of the following.
MN = ___________
NP = ______________
PQ = _________
MQ = _____________
E
For Exercises 10 – 11, refer to the figure to the right. 
V
W
10. Find m Ð WUY.
X
Given:
m Ð VUW = 20o
m Ð YUX = 50o
m Ð XUW = 55o
11. Find m Ð TUV.
T
Y
U
12. Find the midpoint of a segment with endpoints X(11, -5) and Y(8, -14).
13. BD bisects Ð ABC. If m Ð ABD = 63o, what is m Ð ABC?
V
For Exercises 14 – 16, refer to the figure to the right. 
X
14. Name two pairs of angles that form a linear pair?
Which angles are supplementary?
2
1
T
15. Which angles are vertical angles?
5
3
4
16. If m Ð 1 = (6x – 20)o, m Ð 5 = (7y + 12)o, and
m Ð 4 = (3x + 7)o, Find the value of y.
17. Two angles are complementary. One angle has a measure that is
twice the other angle. What is the measure of the smaller angle?
18. Two angles are supplementary. One angle is 5 times the other angle. What is the larger
angle?
19. Classify the transformation as a rotation, reflection, or translation.
a)
b)
20. Consider the translation that is defined by the coordinate notation (x, y)(x – 4, y+ 4).
What are the coordinates of the image of each of the following:
a) A(2, -2)
b) B(-1, 3)
c) C(5, 7)
Y
21. Sketch the image of A(-2, 7) after a composition using the following transformations.
a) Reflection: in the x-axis
Rotation: 90o clockwise about the origin
b) Reflection: in the y-axis
Translation: (x, y)  (x – 2, y – 4)
c) Rotation: 90o clockwise about the origin
Translation: (x, y)  (x – 5, y + 3)
22. What is the if-then form of “A group is a dozen if it has 12 objects?”
23. What is the inverse of “If it rains, then sidewalk is wet?”
24. What is the contrapositive of “If x = 7, then 3x + 3 = 24?”
25. What is the biconditional form of the statement “All dogs bark?”
26. Write each statement below as a biconditional statement, if possible
a) If two lines do not intersect, then they are parallel.
b) If two angles are complementary, then they add up to 90.
c) If two angles are a linear pair, then they are supplementary.
27. Identify the conclusion that can be reached and tell which law of logic allows the
conclusion to be made given the true statements #1 and #2 below?
a) Statement #1: If two lines are perpendicular, then they form right angles.
Statement #2: If two lines form right angles, then the angles are 90.
Conclusion: ________________________________________________________.
Law of Logic ______________________________________
b) Statement #1: If you study for the test, then you will get a good grade.
Statement #2: Art studied for the test.
Conclusion: ________________________________________________________
Law of Logic ______________________________________________
28. Which property of equality matches each conditional statement:
a) If x = 15, then x + 3 = 18. _______________________________
b) If x = 12, then 5x = 60
________________________________
c) If x + y = 14, then 14 = x + y _____________________________
d) If x = n and n = 7, then x = 7 ______________________________
29. In the figure to the right, WX @ YZ . Find the length of XZ .
6x + 3
8x - 5
W
27
X
Y
Z
30. Two angles, Ð 1 and Ð 2, are complementary. If m Ð 1 = 54 , what is m Ð 2?
o
31. Use the figure to the right to find m Ð 2 if m Ð 1 = 41o.
2
1
For Exercises 32 – 33, refer to the figure to the right. 
32. Find m Ð 2 if m Ð 3 = 115o.
1
For Exercises 34 – 37, refer to the figure to the right.
34.
3
2
33. Solve for x if m Ð 4 = (4x + 5)o and m Ð 3 = (6x + 15)o
4

G
F
AB and FG are ________________.
E
35. Which lines are skew to BC ?
36. BC and
H
D
BH are ___________________.
C
A
B
37. Name a line parallel to EG . ______________
For Exercises 38 and 39, refer to the figure to the right. 
38. Find the value of x.
39. Find the value of y.
41°
y
x
40. Use the figure below to determine the type angles shown and what is true
when x || y.
z
a) Ð1 and Ð3; Ð6 and Ð8
___________________________________
1 8
b) mÐ2 and mÐ3
x
2
___________________________________
c) mÐ1 and mÐ5
___________________________________
y
d) mÐ2 and mÐ6
___________________________________
7
79°
46°
I
4
5
M
J
41. Use the figure to the right to determine
which line segments are parallel.
6
3
80°
45°
79°
K
L
N
42. Use the figure to the right to find the
value of x that makes x || y .
110°
x
(4x + 30)°
y
c
43. Which theorem or postulate proves a || b in the figure to the right?
a
b
44. Use the figure below to determine the value of x that makes a || b.
c
3x
(4x + 40)
a
b
45. Write the equation of the line has a y-intercept of 3 and is parallel to the line with
1
equation y = - x + 91.
3
46. Identify each pair of lines as perpendicular, parallel, or neither?
a) y = y=
1
x + 7;
3
1
x–7
3
______________
b) y = 7x + 3:
y = 8x + 3
_________________
c) y = y=
3
x–7
5
1
x+8
2
1
y  x2
2
d) y =
5
x – 23
3
_____________ ______________
47. Given l || m, m Ð 4 = 108o and mÐ10 = 64, use the figure
to the right to find the measure of each angle. 
1 = _______ 2 = _______ 3 = _______
l
m
1
2
5 6
4 = _______ 5 = _______ 6 = _______
10
7 = _______ 8 = _______ 9 = _______
10 = _______ 11 = _______ 12 = _______
13 = _______ 14 = _______ 15 = _______ 16 = _______
9
13 14
3
4
7 8
p
11 12
n
15 16
48. Find the slope of any line that is perpendicular to the line through (-2, 7) and (4, -11).
49. Use the figure to the right to find the value of x.
(4x + 10)°
88°
50. Use the figure to the right to find the value of x.
5x + 5
2x + 14
8x - 17
51. Name the type of triangle described below.
a) At least two congruent sides and an obtuse angle. ___________________
b) three congruent sides. __________________________
c) a right angle and two congruent sides. ___________________________
d) three acute angles and no congruent sides is __________________.
A
D
C
B
52. Given AD^ BD , AC^ BC , and BD @ AC , which
postulate or theorem can be used to prove ACB @ BDA ?
53. Find the measure of Ð1 in the figure to the right.
135
Ð1
54. An isosceles triangle has a perimeter of 64 cm. The lengths of the legs of the triangle
are represented by (4x – 5) and (7x – 26). Find the length of the base of the triangle.
For Exercises 55 and 56, refer to the figure to the right. 
55. Given ÐA @ ÐD and ÐB @ ÐE, find the value of x.
A
30°
B
E
50°
C
56. Find mÐC.
(5x + 30)° F
D
57. In MNO and XYZ, MN @ XY and NO @ YZ . If the two triangles are congruent, what
else must be true to prove the triangles congruent by SAS?
E
58. Use the figure to the right to determine which postulate
or theorem can be used to prove EFH @ GHF?
H
G
F
59. Given that ÐA @ ÐD and ÐB @ ÐE, what is the 3rd congruence needed to prove that
ABC @ DEF by ASA?
60. Tell which postulate or theorem can be used to prove that the triangles are
congruent and give the congruence correspondence of the triangles?
K
L
a)
b)
I
______________________
J
_____________________
41°
61. What are the values of x and y in the figure at the right?
61 in
61 in
x
y
49 in
62. What is the value of x in the figure to the right?
xo
63. Find the m Ð BCD in the figure to the right.
C
m
m
m
D
A
CAB = 30o
ABC = (4x + 10)o
BCD = (6x + 20)o
B
Use the figure to the right for Exercises 64 – 65.
64. Given that F, G, and E are the midpoints of
KL, LM ,and KM respectively, find FG.
4x - 5
L
6x + 2
F
G
K
65. Given that F, G, and E are the midpoints of
KL, LM ,and KM respectively and m Ð EKF = 62o,
find m Ð GFK.
E
14x - 8
M
8
66. In NPR, points O, Q, and S are midpoints
of the sides.
Find the slope and the length of OQ
6
4
and NR in the figure to the right.
P
O
2
Q
N
-10
-5
5
S
10
R
-2
-4
E
55°
67. Using the figure to the right, list the sides
in order from shortest to longest.
-6
42°
F
-8
G
68. A triangle has two sides that have lengths of 12 cm and 25 cm. Name two inequalities
that could represent the length of the third side?
69. Tell if each set of measures will form a triangle?
a) 2 cm, 3cm, 5 cm ______________
b) 20 in., 17 in., 40 in ______________
c) 8.3 ft., 4.3 ft., 4.9 ft._____________
d) 12 cm, 12 cm, 1.5 cm ____________
e) 30.5 in., 58.5 in., 26.5 in. __________
70. In  ABC, mÐA = (3x + 25)°, mÐB = (7x – 9)° , and mÐC = (2x + 20) °.
List the sides of  ABC in order from shortest to longest.
71. Use the diagram below to complete the statement.
a) If x = 27 and y = 26,
then mÐ1 _______mÐ6.
b) If mÐ1 = 100and mÐ6 = 98
Then x ___________y
1
20 in
19 in
3
y
2
x
5
4
19 in
20 in
6
72. Use the figure to the right to choose the inequality that
correctly describes the restriction on the value of x.
22 m
46° 48°
22 m
x+3
2x - 11
73. Use the figure to the right to find the length of NK when
MN = 10 cm and MK = 24 cm.
N
M
K
Geometry
1st Semester Proof Review
Name ________________
1. Given: BC || DE , ÐADE @ ÐAED
Prove: ÐABC @ ÐACB
A
B
C
E
D
2. Given: AB || CD, AD ^ DC , AB ^ BC
Prove: ABC @ CDA
A
B
D
C
H
3. Given: HL and JK bisect each other.
Prove: ÐL @ ÐH
K
J
M
L
P
4. Given: PQ @ PW , QR @ WV
Prove: PR @ PV
Q
R
v
w
5. Given: PQ is an altitude and a median of OPR
Prove: OPR is isosceles
R
O
6. Given: 3(2t + 9) = 30
Prove: t =
½
d
c
7. Given: a || b; c || d
Prove: Ð1 @ Ð12
1
a
2
3 4
5 6
7 8
b
8. Given: Ð AEC @ Ð DEB
Prove: Ð AEB @ Ð DEC
10 11
9 12
A
B
C
E
D
Geometry
1st Semester Review
Name:___________________
Be able to define and understand all of the following terms and concepts.
1. Conjecture
26. Conditional Statements
2. Points
27. Hypothesis and Conclusion
3. Lines
28. Inductive Reasoning
4. Planes
29. Counterexample
5. Segments
30. Converse
6. Rays
31. Inverse
7. Length of a segment (AB)
32. Contrapositive
8. Collinear Points
33. Biconditional statement
9. Coplanar Points
34. Theorem
10. Opposite Rays
35. Law of Detachment
11. Intersection of two lines
36. Law of Syllogism
12. Intersection of two planes
37. Perpendicular Lines
13. Distance Formula
38. Line perpendicular to a plane
14. Midpoint Formula
39. Parallel Lines
15. Betweenness of points
40. Parallel Planes
16. Bisect
41. Transversal
17. Midpoint
42. Alternate Exterior Angles
18. Vertical Angles
43. Alternate Interior Angles
19. Linear Pair
44. Corresponding Angles
20. Complementary Angles
45. Consecutive Interior Angles
21. Supplementary Angles
22. Angle Addition postulate
23. Segment Addition Postulate
24. Angles – acute, right, obtuse
25. Adjacent Angles