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Geometry Review Packet
Semester 1 Final
Name_______________________
Section 1.1
1. Name all the ways you can name the following ray:

B
A
1________________________

C
Section 1.2
What is a(n);
acute angle
2.
right angle
3.
obtuse angle
4.
straight angle
5.
6. Change 41
2
to degrees and minutes.
5
A
7. Given: ABC is a rt. 
mABD = 6721’ 37”
Find: mDBC
D
B
C
Section 1.3
B
8. AC must be smaller than what number?
6
A
10
x
C
9. AC must be larger than what number?
1
10. Can a triangle have sides of length 12, 13, and 26?
Given:
m1 = 2x + 40
m2 = 2y + 40
m3 = x + 2y
Find:
1
2
3
11. m1
12. m2
13. m3
14. EH is divided by F and G in the ratio of 5:3:2 from left to right. If EH = 30, find FG and name the
midpoint of EH .
Section 1.4
Graph the image of quadrilateral SKHD under the following transformations:
15. Reflect across the y-axis
16. Then reflect across the x-axis
Section 1.7
17. What is a postulate? __________________________________________________________
18. What is a definition? __________________________________________________________
19. What is a theorem? __________________________________________________________
2
20. Which of the above (#10 - 12) are reversible? ______________________________________
Section 1.8
21. If a conditional statement is true, then what other statement is also true?
State the converse, inverse, and contrapositive for the following conditional statement:
If Cheryl is a member of the Perry basketball team, then she is a student at Perry.
22. Converse:
23. Inverse:
24. Contrapositive:
25. Place the following statements in order, showing a proper chain of reasoning. Then write a
concluding statement based upon the following information:
ab
d  ~c
~c  a
bf
Section 2.1
26. If AB  BC and 1, 2. and 3 are in the ratio
1:2:3, find the measure of each angle.
Section 2.2
A
1
B
2
3
C
27. One of two complementary angles is twice the other. Find the measures of the angles.
28. The larger of two supplementary angles exceeds 7 times the smaller by 4. Find the measure of the
larger angle.
3
Section 2.5
Given: GH  JK , GH = x + 10
HJ = 8, JK = 2x - 4
29. Find: GJ
G
Section 2.6
30. Given: HGJ  ONP
GJ and NP are bisectors


mHGJ = 25 , mONR = (2x + 10)
Find: x
H
Section 2.8
J
N
K
O
P
R
(3x + 42)
31. Is this possible?
(4x + 45)
Section 3.2
Name the method (if any) of proving the triangles congruent. (SSS, ASA, SAS, AAS, HL)
31.
32.
33.
34.
35.
36.
4
37.
38.
2. Identify the additional information needed to support the method for proving the triangles
congruent.
O
K
HGJ  OMK
G
39. by SAS _______________
40. by ASA _______________
M
41. by HL ________________
J
H
V
PSV  TRV
42. by SAS _______________
43. by ASA _______________
44. by AAS _______________
P
T
S
R
W
ZBW  XAY
Z
A
45. by SSS _______________
46. by SAS _________________
B
X
Y
T
Section 3.4
Given:
TW is a median
ST = x + 40
SW = 2x + 30
WV = 5x – 6
Find: 47. SW
48. WV
49. ST
S
W
V
5
Section 3.6
G
50. If the perimeter of ΔEFG is 32, is ΔEFG scalene,
isosceles, or equilateral?
x+7
10
E
F
2x - 3
A
51. Given: AB and AC are the legs of isosceles ΔABC.
m1 = 5x
m3 = 2x + 12
Find: m2
2
C
3
1
B
52. If the mC is acute, what are the restrictions on x?
(x + 20)°
C
53. Given: m1, m2, m3 are in the ratio 6:5:4.
Find the measure of each angle.
1
54. If ΔHIK is equilateral, what are the values of x and y?
2
3
H
15
I
x+8
1
y6
3
K
6
Section 3.7
Q
55. Given: mP + mR < 180°
PQ < QR
Write an inequality describing the
restrictions on x.
(7x – 18)°
P
(4x)°
R
A
56. Given: AB  AC
Solve for x.
B
(x2 –6x)°
55°
C
Section 4.1
Find the coordinates of the midpoint of each side of ABC.
57. Midpoint of AB =
A (-4, 3)
B (6, 5)
58. Midpoint of BC =
C (6, -1)
59. Midpoint of AC =
60. Find the coordinates of B, a point on circle O.
B (x, y)
O (7, 6)
A (6, 2)
Section 4.3
61. If squares A and C are folded across the dotted segments onto B, find the area of B that will not be
covered by either square.
18
4
A
B
C
7
62. Is b  a? Justify your answer.
b
a
Section 4.6
63. AB has a slope of
2x  37 2x  y 
3y  21
5
. If A = (2, 7) and B = (12, c), what is the value of c?
2
Use slopes to justify your answers to the following questions.
C (9, 8)
64. Is RE || TC ?
T (-3, 4)
65. Is TR || CE ?
E (10, 5)
R (-2, 1)
66. Show that R is a right angle.
Given the diagram as marked, with AC an altitude and AD a median, find the slope of each line.
67. BE
A (5, 9)
68. AC
69. AD
E (11, 3)
B (3, 1)
C
D
70. A line through A and parallel to BE .
8
Section 5.1
Use the diagram on the right for #71 - 75.
Identify each of the following pairs of angles as alternate interior, alternate exterior, or corresponding.
71. For BE and CD with transversal BC ,
E
D
1 and C are _________________.
5
4
72. For AE and BD with transversal BE ,
2 and 4 are _________________.
If AE || BD is:
73. 4  C?
1
A
2
3
B
74. 4  3?
C
75. 4  2?
Q
Section 5.2
R
1
76. If 1  2, which lines are parallel?
2
S
P
77. Write an inequality stating the restrictions on x.
3
x  50
Section 5.3
78. Are e and f parallel?
5x  20
79. Given: a || b
m1 = x  3y 
3x  30
a
2
m2 = 2x  30
m3 = 5y  20
Find: m1
e
2x  10
b
f
1
3
9
80. If f || g, find m1.
f
70
1
100
81. Given: AD || BC
Name all pairs of angles that must be congruent.
D
2 3
A
Sections 5.4 – 5.7
82. ABCD is a
Find the perimeter of ABCD.
g
4
6
1
A
2x + 6
C
5
B
B
8
D
83. Given: mIPT = 5x – 10
KP = 6x
Find KT
K
I
x+8
C
T
P
E
84. Given:
M
KMOP
O
mM = x  3y 
mO = x  4
mP = 4 y  8
Find: mK
K
P
10
R
E
85. Given: RECT is a rectangle
RA = 43x
AC = 214x – 742
Find: The length of ET to the nearest tenth.
A
T
Sect. 6.1-6.2
C
86. a  b = ________
87. ET and point _______ determine plane b.
a
E
G
88. M, E and T determine plane ________
b
O
M
Y
89. TE and GM determine plane ________
T
R
90. Name the foot of OR in a. ________
91. Is M on plane b ? ________
W
92. Given: WY  XY
1
WYZ = x + 68
3
WYX = 2x – 30
Is WY  a ?
Sect. 6.3
a
Y
X
n
A
93. Is ABCD a plane figure?
94. If m || n, is AB || CD?
Z
D
B
95. If AB || CD, is m || n ?
m
C
True or False.
96. _____ Two lines must either intersect or be parallel.
97. _____ In a plane, two lines  to the same line must be parallel.
98. _____ In space, two lines  to the same line are parallel.
99. _____ If a line is  to a plane, it is  to all lines on the plane.
11
100. _____ Two planes can intersect at a point.
101. _____ If a line is  to a line in a plane, it is  to the plane.
102. _____ If two lines are  to the same line, they are parallel.
103. _____ A triangle is a plane figure.
104. _____ Three parallel lines must be co-planar.
105. _____ Every four-sided figure is a plane figure.
Sect 7.1
5
6 4
106. Given: 5 = 70
3 = 130
Find the measures of all the angles.
2
1
3
X
107. Given: Diagram as shown
Find: AB and W
40
80
A
W
108. Find the restrictions on x.
26
B
Y
(4x + 12)
120
109. The measures of the 3 ’s of a  are in the ratio 2:3:5. Find the measure of each angle.
110. Given: T = 2x + 6
RSU = 4x + 16
R = x + 48
Find: mT
R
Sect. 7.2
111. Given: A  D
B is the midpoint of CE
Is ABC  DBE? If so, by which theorem?
S
T
U
A
E
B
C
D
12
I
112. If I  A, is IFA  NLA ?
If so, by which theorem?
Sect. 7.3
A
N
F
L
113. Find the sum of the measures of the angles in a 14-gon.
114. What is the sum of the measures of the exterior angles of an octagon?
115. Find the number of diagonals in a 12-sided polygon.
116. Determine the number of sides a polygon has if the sum of the interior angles is 2340.
Sect 7.4
117. Find the measure of each exterior angle of a regular 20-gon.
118. Find the measure of an angle in a regular nonagon.
119. Find the sum of the measures of the angles of a regular polygon if each exterior angle measures 30.
Sections 1.1 - 7.4
Sometimes, Always or Never (S, A, or N)
___ 120. The triangles are congruent if two sides and an angle of one are congruent to the
corresponding parts of the other.
___ 121. If two sides of a right triangle are congruent to the corresponding parts of another right
triangle, the triangles are congruent.
___ 122. All three altitudes of a triangle fall outside the triangle.
___ 123. A right triangle is congruent to an obtuse triangle.
___ 124. If a triangle is obtuse, it is isosceles.
___ 125. The bisector of the vertex angle of a scalene triangle is perpendicular to the base.
___ 126. The acute angles of a right triangle are complementary.
13
___ 127. The supplement of one of the angles of a triangle is equal in measure to the sum of the other
two angles of the triangle.
___ 128. A triangle contains two obtuse angles.
___ 129. A triangle is a plane figure.
___ 130. Supplements of complementary angles are congruent.
___ 131. If one of the angles of an isosceles triangle is 60, the triangle is equilateral.
___ 132. If the sides of one triangle are doubled to form another triangle, each angle of the second
triangle is twice as large as the corresponding angle of the first triangle.
___ 133. If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid.
___ 134. If the diagonals of a quadrilateral divide each angle into two 45-degree angles, the
quadrilateral is a square.
___ 135. If a parallelogram is equilateral, it is equiangular.
___ 136. If two of the angles of a trapezoid are congruent, the trapezoid is isosceles.
___ 137. A square is a rhombus
___ 138. A rhombus is a square.
___ 139. A kite is a parallelogram.
___ 140. A rectangle is a polygon.
___ 141. A polygon has the same number of vertices as sides.
___ 142. A parallelogram has three diagonals.
___ 143. A trapezoid has three bases.
___ 144. A quadrilateral is a parallelogram if the diagonals are congruent.
___ 145. A quadrilateral is a parallelogram if one pair of opposite sides is congruent and one pair of
opposite sides is parallel.
___ 146. A quadrilateral is a parallelogram if each pair of consecutive angles is supplementary.
___ 147. A quadrilateral is a parallelogram if all angles are right angles.
14
___ 148. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the
quadrilateral is a kite.
___ 149. Two parallel lines determine a plane.
___ 150. If a plane contains one of two skew lines, it contains the other.
___ 151. If a line and a plane never meet, they are parallel.
___ 152. If two parallel lines lie in different planes, the planes are parallel.
___ 153. If a line is perpendicular to two planes, the planes are parallel.
___ 154. If a plane and a line not in the plane are each perpendicular to the same line, then they are
parallel to each other.
___ 155. In a plane, two lines perpendicular to the same line are parallel.
___ 156. In space, two lines perpendicular to the same line are parallel.
___ 157. If a line is perpendicular to a plane, it is perpendicular to every line in the plane.
___ 158. If a line is perpendicular to a line in a plane, it is perpendicular to the plane.
___ 159. Two lines perpendicular to the same line are parallel.
___ 160. Three parallel lines are coplanar.
Geometry Final Proof Review
A
161. Given:  BAC   ACD
 BCA   DAC
 EDA   ABC
Prove: ABCD is a rectangle
E
B
D
C
C
162. Given: CD  m
 ABC is isosceles, with base AB
Prove:  DAB   DBA
m
A
D
B
15
B
D
163. Given: AE is an altitude
E
FD is an altitude
ABDC is a parallelogram
F
Prove: BF  EC
A
C
A
B
164. Given: AE  EB
DE  EC
Prove:  ACD
  BDC
E
D
C
165. Given:  A
AC is an altitude
a
A
Prove: AC is a median
B
166. Given: ACEG is a rectangle
B, D, F & H are midpoints
A
C
B
D
C
H
D
Prove: BHFD is a parallelogram
G
F
E
16
A
167. Given:  O, BO is an altitude
O
B
Prove: AB  CB
C
A
C
168. Given: AE  ED
CD  ED
<AEF  <CDF
Prove: AD
F
 EC
E
D
A
169. Given:  ACE is isosceles with base CE
B, D, F are midpoints
Prove:  ABD
B
F
  AFD
C
E
S
170. Given: 1 is complementary to 4
2 is complementary to 3
RT bisects  SRV
Prove:  S   V
D
R
3
4
1
2
T
V
17
A
171. Given:  ABC is isosceles with base BC
BF  CG , FH  BC , GI  BC
 OFG   OGF
Prove:  HFO   IGO
F
B
A
H
O
R
172. Given: Diagram as shown
1  4
Prove:  2
G
1
I
T
2
3
C
S
4
 3
K
173. Given: OP  RS
KO  KS
M is the midpoint of OK
T is the midpoint of KS
M
T
Prove: MP  TR
O
 ST
NP  VT
P  T
R
P
174. Given: PR
Prove:  WRS is isosceles
P
S
T
W
N
S
R
V
18
175. Given:  XYZ is isosceles with base YZ
X
A, B trisect YZ
Prove: XA  XB
Y
A
176. Given: P is the midpoint of XZ
1  2
Prove: XY
 YZ
B
Z
Z
1
W
Y
P
2
X
A
177. Given: AF || EC
AF  EC
BE  FD
D
F
E
Prove: ABCD is a parallelogram
B
C
19