Geometry 1st Semester Exam Review 2011
I. Definitions
1. conjecture –
2. segment 3. ray 4. postulate 5. acute angle 6. right angle –
7. obtuse angle –
8. straight angle –
9. segment bisector –
10. angle bisector –
11. vertical angles –
12. complementary angles –
13. supplementary angles –
14. counterexample –
15. linear pair –
16. converse –
17. inverse –
18. contrapositive –
19. biconditional statement –
20. perpendicular lines 21. parallel lines –
22. skew lines –
23. transversal –
24. alternate interior angles –
Geometry 1st Semester Exam Review 2011
25. alternate exterior angles –
26. consecutive interior angles –
27. midpoint –
28. isosceles triangle –
29. right triangle –
30. obtuse triangle –
31. acute triangle –
32. scalene triangle –
33. equilateral triangle –
34. polygon –
35. perpendicular bisector –
36. concurrent lines –
37. circumcenter –
38. incenter –
39. median –
40. centroid –
41. altitude –
42. orthocenter –
43. convex –
44. concave –
45. regular –
46. parallelogram –
47. rhombus –
48. square –
49. rectangle –
Geometry 1st Semester Exam Review 2011
II. Quadrilateral Properties
Parallelogram
Rectangle
Rhombus
Square
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.
59. Diagonals are
.
III. Proofs
Given: AB = BC
Prove: ½ AC = BC
Statements
Reasons
1. AB = BC
60.
2. AC = AB + BC
61.
3. AC = BC + BC
62.
4. AC = 2 BC
63
5. ½ AC = BC
64.
Geometry 1st Semester Exam Review 2011
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 3
4 2
Reasons
65.
2. 1 and 3 are supplementary
2 and 3 are supplementary
66.
3. m 1 + m 3 = 180
m 2 + m 3 = 180
4. m 1 = m 2
67.
68.
Given: AB  BC
ABC is bisected by BD
Prove: ∆ABD  ∆CBD
Statements
Reasons
1. AB  BC
1. Given
69. _____________________________
2. Definition of  Bisector
3. BD  BD
70. ________________________
4. ∆ABD  ∆CBD
71. ________________________
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. ________________________
3. ∆DFC  ∆DFE
73. ________________________
Geometry 1st Semester Exam Review 2011
IV. Problems
Find the measure of each variable.
74.
75.
21
44
76.
21
y
x
4x-60
30
6x
Find the measure of each angle.
1
43
77. 1
4
56
78. 2
79. 3
80. 4
81. 5
5
2
3
82. 6
78
6
Determine whether the following triangles are congruent. (SSS, SAS, ASA, AAS, cannot be determined)
83.
84.
85.
Use the conditional statement to identify the following.
If an angle measures less than 90, then it is an acute angle.
86. Hypothesis: __________________________________________________________________________
87. Conclusion: __________________________________________________________________________
88. Converse: ___________________________________________________________________________
89. Inverse: _____________________________________________________________________________
90. Contrapositive: _______________________________________________________________________
Geometry 1st Semester Exam Review 2011
G is the centroid of ABC, AD = 15, CG = 13 and AD  CB.
A
91. Find the length of AG.
92. Find the length of GD.
F
E
93. Find the length of GE.
G
94. Find the length of GB.
B
C
D
List the angles of the triangle in order from least to greatest.
95.
96.
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
98. XZ = 9, YZ = 5
Use the figure below to determine if the segments are parallel, skew, or perpendicular.
H
G
A
99. AB and AH
100. EF and AC
B
G
101. DF and BG
E
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
Geometry 1st Semester Exam Review 2011
Find the value of the variables.
107.
108.
2x + 50
3x + 17
5x - 10
4x - 22
Use the diagram to answer the following questions.
K
109. Name a point collinear to K.
R
110. Name a point coplanar to P.
L
Q
O
M
N
P
111.
112.
110
y + 20
2x + 8
70 
2x + 40
113.
3x + 17
5y + 15
8y + 36
64 
48 + x
14y - 24
Geometry 1st Semester Exam Review 2011
Find the missing measure(s) for the given trapezoid.
114. For trapezoid ADFC, B and E are
midpoints of the legs. Find AD.
115. For trapezoid WXYZ, P and Q are
midpoints of the legs. Find WX.
AD = _______
WX = _______
A
D
W
72
B
E
C
12
P
F
Q
Z
Y
19
86
116. For trapezoid DEFG, T and U are
midpoints of the legs. Find TU, mE.
mG.
TU = ______, mE = _______, mG = _______
42
D
X
E
35
117. For isosceles trapezoid QRST, find
AB, mQ, and mS.
AB = ________, mQ = ________, mS = ________
60
T
S
U
T
85
G
14
125
F
Q
25
R
*** Make sure that you look over your Study Guide from Chapter 6! I didn’t really put questions from Chapter 6 on
the exam study guide since we just took the Ch 6 Test on Wednesday.