Name_______________________
Geometry 1st Semester Review
*Be sure to know how to work out the multiple choice questions.
The final will consist of multiple choice and free response questions.
Chapter 1
1. Which term describes ∠LMP?
A. acute
B. obtuse
2. What is m∠WXY?
A. 20˚
C. 60˚
B. 40˚
D. 100˚
3. Which pair of angles is adjacent?
A. ∠1 and ∠2
B. ∠1 and ∠3
4. If m∠A  47˚, what is the measure of a complement of ∠A?
A. 43˚
B. 133˚
5. What is the area of a triangle with a base of 6 inches and a height of 3 inches?
A. 9 in2
B. 18 in2
6. What is the approximate area of a circle with a radius of 4 feet? Use 3.14 for .
A. 12.56 ft2
C. 50.24 ft2
B. 25.12 ft2
D. 200.96 ft2
7. What are the coordinates of the midpoint of GH with endpoints G(2, 5) and H(4, 1)?
A. (6, 4)
C. (3, 2)
B. (1, 3)
D. (2, 6)
8. Use the Distance Formula to find VW.
A. 5
B.
C. 9
29
D. 25
9. Use the Pythagorean Theorem to find the length of the hypotenuse.
A. 10
C. 48
B. 14
D. 100
10. Which segment is on line n?
F. AD
H. AC
G. BC
J. BE
11. Which is the name of a ray with endpoint A?
A. DA
C. CA
B. BC
D. AB
12. What is the measure of RT ?
A. 5
C. 26
B. 16
D. 40
13. Which term describes ∠PMQ?
A. obtuse
C. right
B. straight
D. acute
14. What is m∠PMN?
F. 22˚
G. 90˚
H. 68˚
J. 112˚
15. Which angles are adjacent and form a linear pair?
A. ∠1 and ∠2
C. ∠2 and ∠3
B. ∠3 and ∠4
D. ∠1 and ∠5
16. What is the area of a triangle with a height of 3 inches and a base of 5.5 inches?
A. 8.25 in2
2
B. 8.5 in
C. 16.5 in.
D. 16.5 in2
17. A circle has a diameter of 10 feet. What is its approximate area?
F. 314.5 ft2
H. 50.24 ft2
G. 87.54 ft2
J. 78.54 ft2
18. Given GH with endpoints G(11, 4) and H(1, 9), what are the coordinates of the midpoint of GH ?
A. (12, 5)
C. (10, 13)
B. (6, 2.5)
D. (5, 6.5)
19. What is the distance from M(1, 6) to N(11, 1)?
A. 12 units
C. 13 units
B.
D. 169 units
149 units
20. What is the distance from V to W?
F. 17 cm
H. 120 cm
G. 23 cm
J. 289 cm
Chapter 2
Circle the best answer.
21. Which conditional statement is true?
A. If two angles are acute, then they are complementary.
B. If an angle is acute, then its measure is less than 90o.
22. What is the converse of “If there are clouds in the sky, then it is raining”?
A. If it is raining, then there are clouds in the sky.
B. If it is not raining, then there are clouds in the sky.
C. If it is raining, then there are no clouds in the sky.
D. If it is not raining, then there are no clouds in the sky.
23. Given: Pluto is the only planet other than Earth with only one moon. A student is looking through a telescope at a
planet that has only one moon. What conclusion can be drawn?
A. The student is not looking at Pluto.
B. The student is looking at Pluto.
24. Given: If two angles are complementary, then both angles measure less than 90o. Angles that measure less than 90o
are acute.  1 and  2 are complementary. What conclusion can be drawn?
A. Only  1 is acute.
B. Only  2 is acute.
C. Both angles are acute.
D. Neither angle is acute.
25. What is the contrapositive of “If there are clouds in the sky, then it is raining”?
A. If it is raining, then there are clouds in the sky.
B. If it is not raining, then there are clouds in the sky.
C. If it is raining, then there are no clouds in the sky.
D. If it is not raining, then there are no clouds in the sky.
26. Which property is used in solving y + 3 =11?
A. Symm. Prop. of =
B. Div. Prop. of =
C. Mult. Prop. of =
D. Subtr. Prop. of =
27. Which is an example of the Reflexive Property of Congruence?
A. AB  EF
B. EF  EF
28.Given the partially completed two-column proof, which is the reason for Step 3?
Statements
Reasons
1. AE  FB
1. Given
2. FB  EF
2. Given
3. AE  EF
3.
?
Circle the best answer.
29. What is the next item in the pattern?
-1, 2, -4, 8, . . .
A. -16
C. 4
B. -4
D. 16
A. Def. of midpoint
B. Trans. Prop. of 
30. Which is a counterexample that shows that the following conjecture is false: “If  1 and  2 are supplementary,
then one of the angles is obtuse”?
F. m  1=45o and m  2 = 45o
G. m  1 = 53o and m  2 = 127o
H. m  1 = 90o and m  2 = 90o
J. m  1 = 100o and m  2 = 80o
31. What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?
A. If a number is divisible by 3, then it is divisible by 6.
B. If a number is not divisible by 6, then it is not divisible by 3.
C. If a number is not divisible by 3, then it is not divisible by 6.
D. If a number is not divisible by 6, then it is divisible by 3.
32. Given: If one angle of a triangle is a right angle, then the other two angles are both acute. A triangle has a 45o angle.
What conclusion can be drawn?
F. One of the other two angles is 90o.
G. One of the other two angles is obtuse.
H. All three angles are acute.
J. No conclusion can be drawn.
33. Identify the property that justifies the statement “∠N ≅ ∠N ”
F. Addition Prop. of 
G. Reflex. Prop. of 
H. Trans. Prop. of 
J. Sym. Prop. of 
34. Which property is NOT used when solving 3x + 15 = 2x – 1?
A. Subtraction Prop.
B. Add. Prop. of =
C. Div. Prop. of =
D. Sym. Prop. of =
35. Identify the property that justifies the statement “If ∠B  ∠A, then ∠A  ∠B.”
F. Addition Prop. of 
G. Reflex. Prop. of 
H. Trans. Prop. of 
J. Sym. Prop. of 
36. Complete a two column proof for the following.
Given:
are supplementary, and
are supplementary.
Prove:
________STATEMENT____________________________REASON___________________
37. Complete a two column proof for the following.
Given: ∠2 ≅ ∠3
Prove: ∠1 ≅ ∠4
1
2
3
4
N
1
________STATEMENT____________________________REASON___________________
For 38 and 39, Find the measure and name the theorem that justifies your answer.
38. Given that AD = 36, find AB.
A
B
2x  4
C
D
5x  2
39. Find m∠ABC
D
A
B
(6 x  1)
(14 x)

E
C
40.
E
Given: B is the midpoint of AC and AB  EF.
F
Prove: BC  EF
A
B
C
Statement
Chapter 3
41. Given: l || m, 1  3
Prove: j || d
Reason
l
j
1
m
d
2
3
___________STATEMENT_____________________________REASON____________________
Use the figure to identify each of the following.
G
F
42. a pair of skew segments: _______________
H
B
43. a pair of parallel segments: _____________
44. a pair of perpendicular segments: _______
A
W
T
Identify each angle pair.
45. ∠1 and ∠7: _______________________
2
4
1
46. ∠4 and ∠8:_______________________
5
47. ∠4 and ∠7: _______________________
7
6
48. ∠2 and ∠6: _______________________
3
8
49. ∠1 and ∠6: _______________________
50. Solve for x and find each angle measure.
50a. x = _____________________________
A
50b. m∠ABH = ______________________
C
50c. m∠CDF = ______________________
3x+11
H
B
E
9x-61
D
F
S
51. Solve for x and find each angle measure.
51a. x = _______________________
K
51b. m∠STA = __________________
S
T
51c. m∠KAT = __________________
12x A
12x+3
3
9x
D
E
52. Find the slope of the line that passes through the points (-2,4) and (6,8).
52. m= ___________
53. Write the equation of the line through (-6,-2) and (3,4) in point-slope form and slope-intercept form.
Point-slope form__________________
Slope-int. form ___________________
54. Determine whether 6x + y = 3 and 12x + 2y = 6 are parallel, intersect, or coincide.
54. _________________________
Chapter 4
Circle the best answer.
55. What type of triangle is ∆ABC?
A. acute
B. equiangular
C. obtuse
D. right
56. Which pair of angle measures CANNOT be the acute angles of a right triangle?
A. 29o and 61o
B. 30o and 60o
C. 38o and 53o
D. 45o and 45o
57. What is m  ACD?
A. 100
B. 130
58. If ∆KLM  ∆RST, find the value of x.
A. 18
B. 45
59. What additional information would allow you to prove the triangles congruent by AAS?
A.  BEA   D
B.  D   C
C.  D   A
D.  A   C
60. Which postulate or theorem can you use to prove ∆ABE  ∆CDE?
A. SSS
B. SAS
C. ASA
D. AAS
61. What additional information will prove ∆ABE  ∆CDE by HL?
A. AB  CD
B. AE  CE
Circle the best answer.
62. Classify the triangle.
F. isosceles acute
G. isosceles obtuse
H. scalene acute
J. scalene obtuse
63. What is the length of side BC ?
A. 3
C. 10
B. 8
D. 24
Use the figure for Exercises 64 and 65.
64. What is m∠KLM?
F. 3
H. 42
G. 22
J. 64
65. What is m∠M?
A. 0.2˚
C. 26˚
B. 4˚
D. 64˚
66.What is the m∠U?
F. 5˚
G. 15˚
H. 40˚
J. 120˚
67.∆KLM  ∆RST. m∠L = (3x + 15)o and m∠S = (6x + 3)o. What is the value of x?
F. 2
G. 4
H. 6
J. 27
Use the figure for Exercises 68-69.
68. If AD = 5y + 7 and BC = 7y – 3 , what must the value of y be to prove ∆AED  ∆CEB by the SSS Postulate?
A. 2
C. 17
B. 5
D. 32
69. What postulate or theorem justifies the congruence statement ∆ABE  ∆CDE?
F. SSS
H. ASA
G. SAS
J. AAS
70. What is the value of x?
71.
A. 12
C. 18
B. 19.5
D. 60
Given: K  M, K L J  M L J
Prove: JKL  JML
Statement
Reason
72.
Given: AB ≅ BC; BD bisects ∠B.
Prove: ∠A ≅ ∠C
Statement
B
Reason
A
D
Chapter 5
Use the figure to the right for 73-76
73. Given that line p is the perpendicular bisector of
XZ and XY = 12, find ZY. _____________________
74. Given that XZ = 34, YX = 22, and YZ = 22,
find ZW. _____________________
75. Given that line p is the perpendicular bisector of XZ; XY = 8n-5,
and YZ = 35, find n. _____________________
76. Given that XY = ZY, WX = 3x – 1, and XZ 5x + 16, find ZW. _____________________
Use the figure to the right for 77-79.
77. Given that FG = HG and m  FEH = 66˚, find
m  HGE. _____________________
78. Given that EG bisects  FEH and GF = 11 find GH.
_____________________
79. Given that  FEG   GEH, FG = 5x – 15, and
HG = 3.5x + 3, find FG. _____________________
Write an equation in point-slope form for the perpendicular bisector of the segment with the
given endpoints.
80. L(-3, 6), M(1, 2)
__________________________
81. T(-3, -2), U(3, 0)
_______________________________
C
Use the figure for Exercises 82-85. GB  13 and CD  10.
Find each length.
82. FG _________________
83. BF _________________
84. GD _________________
85. CG _________________
Find the centroid of the triangle with the given vertices.
86. X(-5, 4), Y(2, -3), Z(1, 4)
87. (0, -1), B(2, -3), C(4, -1)
(_________, _________)
(_________, _________)
88. Draw an obtuse triangle and all three of the altitudes for the triangle.
89. Draw a right triangle and all three of the medians for the triangle.
Use the Triangle Midsegment Theorem to name parts of
the figure for Exercises 90-94.
90. a midsegment of ABC
_____________________
91. a segment parallel to AC
_____________________
92. a segment that has the same length as BD
_____________________
93. a segment that has half the length of AC
_____________________
94. a segment that has twice the length of EC
_____________________
Use the figure for Exercises 95-100. Find each measure.
22
15
95. HI ___________________
96. DF ___________________
97. GE ___________________
98. m  HIF ___________________
99. m  HGD ___________________ 100. m  D ___________________
101. Write the angles of DEF in order from smallest to largest.
102. Write the sides of GHI in order from shortest to longest.
Tell whether a triangle can have sides with the given lengths.
If not, explain why not.
103. 8, 8, 16 _______________
104. 0.5, 0.7, 0.3 ________
1
105. 10 , 4, 14 ________
2
106. 3x + 2, x2, 2x when x = 4 _______________________
107. 3x + 2, x2, 2x when x = 6 _______________________
The lengths of two sides of a triangle are given. Find the range of possible lengths for the third
side.
108. 8.2 m, 3.5 m
109. 298 ft, 177 ft
110. 3 mi, 4 mi
Find the value of x. Give your answer in simplest radical form.
111.
112.
______________________
113.
______________________
______________________
Find the missing side lengths. Give your answer in simplest radical form. Tell whether the side
lengths form a Pythagorean Triple.
114.
115.
______________________
116.
______________________
______________________
Tell whether the measures can be the side lengths of a triangle. If so, classify the triangle as
acute, obtuse, or right.
117. 15, 18, 20
118. 7, 8, 11
______________________
119. 6, 7, 3 13
______________________
______________________
Find the value of x in each figure. Give your answer in simplest radical form.
120.
121.
______________________
122.
______________________
______________________
Find the values of x and y. Give your answers in simplest radical form.
123. x = _______ y = _______
124. x = _______ y = _______
125. x = _______ y = _______
Constructions: Complete each construction.
126. Copy the given segment.
127. Construct the segment bisector of the given segment.
128. Copy an angle congruent to the angle given.
129. Construct the angle bisector.
130. Construct the perpendicular bisector of the given segment.
131. Construct a line parallel to the given line.