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 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)
6. Use the Distance Formula to find VW.
A. 5
B.
C. 9
29
D. 25
7. Use the Pythagorean Theorem to find the length of the hypotenuse.
A. 10
C. 48
B. 14
D. 100
8. Which segment is on line n?
F. AD
H. AC
G. BC
J. BE
9. Which is the name of a ray with endpoint A?
A. DA
C. CA
B. BC
D. AB
10. What is the measure of RT ?
A. 5
C. 26
B. 16
D. 40
11. Which term describes ∠PMQ?
A. obtuse
C. right
B. straight
D. acute
12. What is m∠PMN?
F. 22˚
G. 90˚
H. 68˚
J. 112˚
13. 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
14. 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)
15. What is the distance from M(1, 6) to N(11, 1)?
A. 12 units
C. 13 units
B.
D. 169 units
149 units
Chapter 2
Circle the best answer.
16. 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.
17. 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.
18.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.
19.Which is an example of the Reflexive Property of Congruence?
A. AB  EF
B. EF  EF
20. 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.
21.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 
Use the figure to identify each of the following.
G
F
22. a pair of skew segments: _______________
H
B
23. a pair of parallel segments: _____________
24. a pair of perpendicular segments: _______
A
W
T
Identify each angle pair.
25. ∠1 and ∠7: _______________________
2
4
1
26. ∠4 and ∠8:_______________________
5
27. ∠4 and ∠7: _______________________
7
6
28. ∠2 and ∠6: _______________________
3
8
29. ∠1 and ∠6: _______________________
30. Solve for x and find each angle measure.
a. x = _____________________________
A
b. m∠ABH = ______________________
C
c. m∠CDF = ______________________
27x+10
H
B
E
D 9x2-82 F
S
31. Solve for x and find each angle measure.
a. x = _______________________
K
b. m∠STA = __________________
S
c. m∠KAT = __________________
12x A
360
T
x2
D
E
Chapter 4
Circle the best answer.
32.What type of triangle is ∆ABC?
A. acute
B. equiangular
C. obtuse
D. right
33. 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
34. What is m  ACD?
A. 100
B. 130
35. If ∆KLM  ∆RST, find the value of x.
A. 18
B. 45
36. 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
37. Which postulate or theorem can you use to prove ∆ABE  ∆CDE?
A. SSS
B. SAS
C. ASA
D. AAS
38. What additional information will prove ∆ABE  ∆CDE by HL?
A. AB  CD
B. AE  CE
Circle the best answer.
39. Classify the triangle.
F. isosceles acute
G. isosceles obtuse
H. scalene acute
J. scalene obtuse
40. What is the perimeter of the triangle?
A. 16
C. 152
B. 40
D. 44
Use the figure for Exercises 41 and 42.
41. What is m∠KLM?
F. 3
H. 42
G. 22
J. 64
42. What is m∠M?
A. 0.2˚
C. 26˚
B. 4˚
D. 64˚
43. Find the value for x.
A. 50˚
C. 60˚
B. 70˚
D. 100˚
Use the figure for Exercises 44-46.
44. 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
45. What postulate or theorem justifies the congruence statement ∆ABE  ∆CDE?
F. SSS
H. ASA
G. SAS
J. AAS
46. 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
72.
Reason
Given: AB ≅ BC; BD bisects ∠B.
Prove: ∠A ≅ ∠C
Statement
B
Reason
A
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. _____________________
D
C
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)
__________________________
_______________________________
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 = _______
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.
125. x = _______ y = _______
129. Construct the angle bisector.
130. Construct the perpendicular bisector of the given segment.
131. Construct a line parallel to the given line.