Geometry 2012 – 2013
1st Semester Exam Review Answers
Name _____________________________
I. Definitions
1. conjecture – an educated guess based on known information
2. segment - a measurable part of a line that consists of 2 endpoints and all of the points between them
3. ray – a segment that continues on in one direction
4. postulate – a statement that is accepted as true without proof
5. acute angle – an angle whose measure is less than 90
6. right angle – an angle whose measure is exactly 90
7. obtuse angle – an angle whose measure is more than 90
8. straight angle – an angle whose measure is exactly 180
9. segment bisector – a segment, line, or plane that intersects a segment at its midpoint
10. angle bisector – a ray that divides an angle into two congruent angles
11. vertical angles – two nonadjacent angles formed by two intersecting lines
12. complementary angles – two angles whose sum is 90
13. supplementary angles – two angles whose sum is 180
14. counterexample – an example used to disprove a statement
15. linear pair – a pair of adjacent angles that form a line
16. converse – the statement formed by switching the hypothesis and conclusion of a conditional statement
17. inverse – the statement formed negating the hypothesis and conclusion of a conditional statement
18. contrapositive – the statement formed by switching and negating the hypothesis and conclusion of a conditional
statement
19. perpendicular lines – lines that intersect to form right angles
20. parallel lines – lines that do not intersect
21. skew lines – lines that do not intersect and are not the same plane
22. transversal – a line that intersects two or more lines at different points
23. alternate interior angles – a pair of interior angles that are on opposite sides of the transversal
24. alternate exterior angles – a pair of exterior angles that are on opposite sides of the transversal
25. consecutive interior angles – a pair of interior angles that are on the same side of the transversal
26. midpoint – the point on a segment exactly halfway between the endpoints of a segment
27. isosceles triangle – a triangle with at least two sides congruent
28. right triangle – a triangle with a right angle and two acute angles
29. obtuse triangle – a triangle with an obtuse angle and two acute angles
30. acute triangle – a triangle with all 3 angles acute
31. scalene triangle – a triangle with no sides congruent
32. equilateral triangle – a triangle with all 3 sides congruent
33. polygon – a closed figure
34. perpendicular bisector – a segment that is perpendicular to a side of a triangle at the midpoint
35. concurrent lines – three or more lines that intersect in the same point
36. circumcenter – the point of concurrency of the perpendicular bisector of a triangle
37. incenter – the point of concurrency of the angle bisectors of a triangle
38. median – segment whose endpoints are a vertex and the midpoint of the opposite side
39. centroid – the point of concurrency of the medians of a triangle
40. altitude – a perpendicular segment drawn from a vertex to the opposite side
41. orthocenter – the point of concurrency of the altitudes of a triangle
42. convex – a polygon whose sides do not cave in
43. concave – a polygon whose sides cave in
44. regular – a polygon that is equiangular and equilateral
45. parallelogram – a quadrilateral with both pairs of opposite sides parallel
46. rhombus – a parallelogram with 4 congruent sides
47. square – a parallelogram with 4 congruent sides and 4 right angles
48. rectangle – a parallelogram with 4 right angles
49. trapezoid – a quadrilateral with exactly one pair of parallel sides
50. isosceles trapezoid – a trapezoid whose legs are congruent
II. Quadrilateral Properties
Parallelogram
Rectangle
Rhombus
Square
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
50. Opposite
sides are parallel.
51. Opposite
sides are .
52. Opposite
angles are .
53. Consecutive
interior angles
supplementary.
54. Diagonals
bisect each other.
55. All 4 angles
are right angles.
56. Diagonals are
.
57. All 4 sides are
.
58. Diagonals
bisect opposite
angles.
X
X
X
X
59. Diagonals are
.
X
X
X
X
X
X
III. Proofs
Given: AB = BC
Prove: ½ AC = BC
Statements
Reasons
1. AB = BC
60. Given
2. AC = AB + BC
61. Segment Addition
3. AC = BC + BC
62. Substitution
4. AC = 2 BC
63. Substitution
5. ½ AC = BC
64. Multiplication/Division
Given: 1 and 3 are a linear pair
2 and 3 are a linear pair
Prove: m1 = m2
Statements
1. 1 and 3 are a linear pair
2 and 3 are a linear pair
1
4
3
2
Reasons
65. Given
2. 1 and 3 are supplementary
2 and 3 are supplementary
66. Supplement Thm
3. m 1 + m 3 = 180
m 2 + m 3 = 180
4. m 1 = m 2
67. Def of Supplementary Angles
68. Congruent Supp Thm
Given: AB  BC
ABC is bisected by BD
Prove: ∆ABD  ∆CBD
Statements
Reasons
1. AB  BC
1. Given
69. ABD = CBD
2. Definition of  Bisector
3. BD  BD
70. Reflexive
4. ∆ABD  ∆CBD
71. SAS
G
Given: ∆DGC  ∆DGE, ∆GCF  ∆GEF
Prove: ∆DFC  ∆DFE
Statements
1. ∆DGC  ∆DGE, ∆GCF  ∆GEF
Reasons
1. Given
2. CDG  EDG; CD  ED; CFD  EFD
72. CPCTC
3. ∆DFC  ∆DFE
73. ASA
IV. Problems
Find the measure of each variable.
74. x = 68
21
75. y = 120
44
76. x = 24
21
y
x
4x-60
30
6x
Find the measure of each angle.
1
4
56
43
5
2
3
77. 1
59
78. 2
78
79. 3
102
80. 4
22
81. 5
68
82. 6
34
78
6
Determine whether the following triangles are congruent. (SSS, SAS, ASA, AAS, cannot
be determined)
83. ASA
84. CBD
85. CBD
Use the conditional statement to identify the following.
If an angle measures less than 90, then it is an acute angle.
86. Hypothesis: an angle measures less than 90
87. Conclusion: it is an acute angle
88. Converse: If an angle is an acute angle, then it measures less than 90.
89. Inverse: If an angle does not measure less than 90, then it is not an acute angle.
90. Contrapositive: If an angle is not an acute angle, then it does not measure less than 90.
G is the centroid of ABC, AD = 15, CG = 13 and AD  CB.
A
F
91. Find the length of AG.
10
92. Find the length of GD.
5
93. Find the length of GE.
6.5
94. Find the length of GB.
13
E
G
B
C
D
List the angles of the triangle in order from least to greatest.
95. I, G, H
96. L, K, J
H
K
m LK = 4.29 cm
m HI = 4.54 cm
m HG = 3.17 cm
L
I
m KJ = 2.99 cm
m JL = 3.52 cm
m IG = 5.44 cm
G
J
Find the possible measures for the third side of XYZ.
97. XZ = 6, YZ = 8
2 < x < 14
98. XZ = 9, YZ = 5
4 < x < 14
Use the figure below to determine if the segments are parallel, skew, or perpendicular.
H
G
A
99. AB and AH perpendicular
100. EF and AC skew
B
G
E
101. DF and BG parallel
F
C
D
Use the figure to identify the special angle pair. (alt. int., alt. ext., cons. int., corr., linear pair)
1
3
5
7
6
8
2
4
102.
103.
104.
105.
106.
1 & 8
5 & 6
2 & 6
4 & 5
4 & 6
alternate exterior
linear pair
corresponding
alternate interior
consecutive interior
Find the value of the variables.
107.
x = 20
108. x = 26.4
2x + 50
3x + 17
5x - 10
4x - 22
Use the diagram to answer the following questions.
K
R
L
Q
109. Name a point collinear to K.
M, L, or R
110. Name a point coplanar to P.
O, M, N, Q, R, or L
O
M
N
P
111. x = 35, y = 50
110
y + 20
112. x = 31, y = 11
2x + 8
70 
113. x = 16, y = 10
8y + 36
3x + 17
64 
5y + 15
2x + 40
48 + x
14y - 24
Find the missing measure(s) for the given trapezoid.
114. For trapezoid ADFC, B and E are
midpoints of the legs. Find AD.
AD = 58
115. For trapezoid WXYZ, P and Q are
midpoints of the legs. Find WX.
WX = 5
A
D
W
72
B
E
C
12
P
F
X
Q
Z
Y
19
86
116. For trapezoid DEFG, T and U are
midpoints of the legs. Find TU, mE.
mG.
117. For isosceles trapezoid QRST, find
AB, mQ, and mS.
TU = 28 , mE = 95 , mG = 145
AB = 42.5 , mQ = 125 , mS = 55
42
D
E
60
T
35
S
U
T
85
G
125
F
Q
14
25
R
PRST is a rectangle. Find each measure if m1 = 50.
118. m2 = 40
119. m3 = 40
120. m4 = 50
121. m5 = 100
122. m6 = 40
123. m7 = 80
124. ABCD is a rectangle. If AD = x2 – 7 and BC = 4x + 5, find AD.
x = -2 or x = 6
AD = 29