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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. AB, AC

C
Section 1.2
What is a(n);
2. acute angle
2. An angle less than 90 but greater than 0
3. right angle
3. An angle = 90
4. obtuse angle
4. An angle less than 180 but greater than 90
5. straight angle
5. An angle = 180
6. Change 41
2
to degrees and minutes.
5
41°24’
A
7. Given: ABC is a rt. 
mABD = 6721’ 37”
Find: mDBC
D
B
C
22° 38’ 23”
Section 1.3
B
8. AC must be smaller than what number?
16
6
A
10
x
C
9. AC must be larger than what number?
4
1
10. Can a triangle have sides of length 12, 13, and 26?
No 12 + 13 < 26
Given:
m1 = 2x + 40
m2 = 2y + 40
m3 = x + 2y
Find:
1
2
3
11. m1 = 80
12. m2 = 100
13. m3 = 80
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 .
FG = 9 F is the midpoint
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? An idea that can’t be disproven so is accepted as true.
18. What is a definition? An accepted meaning of a word or phrase.
19. What is a theorem? An idea that is provable.
2
20. Which of the above (#17-19) are reversible? Definitions
Section 1.8
21. If a conditional statement is true, then what other statement is also true?
Contrapositive
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: If Cheryl is a student at Perry, then she is a member of the Perry basketball team.
23. Inverse: If Cheryl is not a member of the Perry basketball team, then she is not a student at Perry.
24. Contrapositive: If Cheryl is not a student at Perry, then she is not a member of the Perry basketball
team.
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
d => f or ~f => ~c
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.
15, 30, 45
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.
30 and 60
28. The larger of two supplementary angles exceeds 7 times the smaller by 4. Find the measure of the
larger angle.
158
3
Section 2.5
Given: GH  JK , GH = x + 10
HJ = 8, JK = 2x - 4
29. Find: GJ
32
G
Section 2.6
30. Given: HGJ  ONP
GJ and NP are bisectors


mHGJ = 25 , mONR = (2x + 10)
Find: x
H
J
N
O
K
P
R
20
Section 2.8
(3x + 42)
31. Is this possible? Yes, x = -3
(4x + 45)
Section 3.2
Name the method (if any) of proving the triangles congruent. (SSS, ASA, SAS, AAS, HL)
31.
32.
SSS
CBT
33.
34.
AAS
SAS
35.
36.
ASA
SAS
4
37.
38.
CBT
HL
2. Identify the additional information needed to support the method for proving the triangles
congruent.
O
K
HGJ  OMK
G
39. by SAS OK = HJ
40. by ASA <G = <M
M
41. by HL KM = GJ
J
H
V
PSV  TRV
42. by SAS PS = TR
43. by ASA <SVP = <TVR
44. by AAS <VSP = <VRT
P
T
S
R
W
ZBW  XAY
Z
A
45. by SSS BW = AY or AW = BY
46. by SAS <BZW = <AXY
B
X
Y
T
Section 3.4
Given:
TW is a median
ST = x + 40
SW = 2x + 30
WV = 5x – 6
Find: 47. SW = 54
48. WV = 54
49. ST = 52
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
Scalene x = 6
E
A
51. Given: AB and AC are the legs of isosceles ΔABC.
m1 = 5x
m3 = 2x + 12
Find: m2
x = 24
60
F
2x - 3
2
C
3
1
B
52. If the mC is acute, what are the restrictions on x?
x < 70 and x > -20
(x + 20)°
C
53. Given: m1, m2, m3 are in the ratio 6:5:4.
Find the measure of each angle.
72, 60, 48
1
54. If ΔHIK is equilateral, what are the values of x and y?
2
3
H
x=7
y = 63
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
6 < x < 18
(4x)°
R
A
56. Given: AB  AC
Solve for x.
x = -5 or 11
B
(x2 –6x)°
55°
C
Section 4.1
Find the coordinates of the midpoint of each side of ABC.
57. Midpoint of AB = (1,4)
A (-4, 3)
B (6, 5)
58. Midpoint of BC = (6,2)
C (6, -1)
59. Midpoint of AC = (1,1)
60. Find the coordinates of B, a point on circle O.
B (x, y)
B(8,10)
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
8 sq units
4
A
B
C
7
62. Is b  a? Justify your answer.
b
Yes. x = 53/2 and y = 37
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
c = 32
Use slopes to justify your answers to the following questions.
C (9, 8)
64. Is RE || TC ?
Yes
T (-3, 4)
65. Is TR || CE ?
Yes
E (10, 5)
R (-2, 1)
66. Show that R is a right angle.
TR = -3
RE = 1/3
Given the diagram as marked, with AC an altitude and AD a median, find the slope of each line.
67. BE = 1/4
A (5, 9)
68. AC = -4
69. AD = -7/2
E (11, 3)
B (3, 1)
C
D
70. A line through A and parallel to BE .
1/4
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 Corresponding.
5
4
72. For AE and BD with transversal BE ,
2 and 4 are AIA.
If AE || BD is:
73. 4  C?
Unknown
1
A
3
B
74. 4  3?
Unknown
C
75. 4  2?
Yes
Q
Section 5.2
R
1
76. If 1  2, which lines are parallel?
PQ and RS
2
2
S
P
77. Write an inequality stating the restrictions on x.
3
-47 < x < 130
x  50
Section 5.3
78. Are e and f parallel?
No
x = 25
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
70
9
80. If f || g, find m1.
f
70
150
1
100
81. Given: AD || BC
Name all pairs of angles that must be congruent.
g
D
2 3
4
C
2 and 5
A
Sections 5.4 – 5.7
82. ABCD is a
Find the perimeter of ABCD.
6
1
A
2x + 6
5
B
B
8
36
D
83. Given: mIPT = 5x – 10
KP = 6x
Find KT
K
I
x+8
C
T
P
240
E
84. Given:
M
KMOP
O
mM = x  3y 
mO = x  4 
mP = 4y  8
Find: mK
K
P
28
10
R
E
85. Given: RECT is a rectangle
RA = 43x
AC = 214x – 742
Find: The length of ET to the nearest tenth. 8.7
A
T
Sect. 6.1-6.2
C
86. a  b = GY
87. ET and point R or O determine plane b.
a
E
G
88. M, E and T determine plane a
b
O
M
Y
89. TE and GM determine plane a
T
R
90. Name the foot of OR in a. Y
91. Is M on plane b ? No
W
92. Given: WY  XY
1
WYZ = x + 68
3
WYX = 2x – 30
Is WY  a ?
No
x = 60
Sect. 6.3
a
Y
X
n
A
93. Is ABCD a plane figure? Yes
94. If m || n, is AB || CD? Yes
Z
D
B
95. If AB || CD, is m || n ? No
m
C
True or False.
96. __F___ Two lines must either intersect or be parallel.
97. __T___ In a plane, two lines  to the same line must be parallel.
98. __F___ In space, two lines  to the same line are parallel.
11
99. __T___ If a line is  to a plane, it is  to all lines on the plane.
100. __F___ Two planes can intersect at a point.
101. __F___ If a line is  to a line in a plane, it is  to the plane.
102. __ F ___ If two lines are  to the same line, they are parallel.
103. __ T ___ A triangle is a plane figure.
104. __ T ___ Three parallel lines must be co-planar.
105. __ T ___ Every four-sided figure is a plane figure.
Sect 7.1
5
106. Given: 5 = 70
3 = 130
Find the measures of all the angles.
60, 50, 130, 110, 70, 70
6 4
2
1
X
107. Given: Diagram as shown
Find: AB and W
40
A
AB = 13
<W = 60
108. Find the restrictions on x.
3
W
-3 < X < 27
80
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.
36, 54, 90
110. Given: T = 2x + 6
R
RSU = 4x + 16
R = x + 48
Find: mT
S
T
82
U
Sect. 7.2
111. Given: A  D
B is the midpoint of CE
Is ABC  DBE? If so, by which theorem? Yes, AAS
C
A
E
B
D
12
I
112. If I  A, is IFA  NLA ?
If so, by which theorem? No Choice Theorem
Sect. 7.3
A
N
F
L
113. Find the sum of the measures of the angles in a 14-gon. 2160
114. What is the sum of the measures of the exterior angles of an octagon? 360
115. Find the number of diagonals in a 12-sided polygon. 54
116. Determine the number of sides a polygon has if the sum of the interior angles is 2340. 15
Sect 7.4
117. Find the measure of each exterior angle of a regular 20-gon. 18
118. Find the measure of an angle in a regular nonagon. 140
119. Find the sum of the measures of the angles of a regular polygon if each exterior angle measures 30.
1800
Sections 1.1 - 7.4
Sometimes, Always or Never (S, A, or N)
__S_ 120. The triangles are congruent if two sides and an angle of one are congruent to the
corresponding parts of the other.
__A_ 121. If two sides of a right triangle are congruent to the corresponding parts of another right
triangle, the triangles are congruent.
_N*__ 122. All three altitudes of a triangle fall outside the triangle.
_N__ 123. A right triangle is congruent to an obtuse triangle.
_ S __ 124. If a triangle is obtuse, it is isosceles.
_N__ 125. The bisector of the vertex angle of a scalene triangle is perpendicular to the base.
_A__ 126. The acute angles of a right triangle are complementary.
13
_A__ 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.
_N__ 128. A triangle contains two obtuse angles.
_A__ 129. A triangle is a plane figure.
_S__ 130. Supplements of complementary angles are congruent.
_ A __ 131. If one of the angles of an isosceles triangle is 60, the triangle is equilateral.
__N_ 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.
_S__ 133. If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid.
_ A __ 134. If the diagonals of a quadrilateral divide each angle into two 45-degree angles, the
quadrilateral is a square.
_S__ 135. If a parallelogram is equilateral, it is equiangular.
_S__ 136. If two of the angles of a trapezoid are congruent, the trapezoid is isosceles.
_ A __ 137. A square is a rhombus
_S__ 138. A rhombus is a square.
_ A __ 139. A kite is a parallelogram.
_ A __ 140. A rectangle is a polygon.
_ A __ 141. A polygon has the same number of vertices as sides.
_N__ 142. A parallelogram has three diagonals.
_N__ 143. A trapezoid has three bases.
_S__ 144. A quadrilateral is a parallelogram if the diagonals are congruent.
_S__ 145. A quadrilateral is a parallelogram if one pair of opposite sides is congruent and one pair of
opposite sides is parallel.
_ A __ 146. A quadrilateral is a parallelogram if each pair of consecutive angles is supplementary.
_ A __ 147. A quadrilateral is a parallelogram if all angles are right angles.
14
_S__ 148. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the
quadrilateral is a kite.
_ A __ 149. Two parallel lines determine a plane.
_N__ 150. If a plane contains one of two skew lines, it contains the other.
_ A __ 151. If a line and a plane never meet, they are parallel.
_S__ 152. If two parallel lines lie in different planes, the planes are parallel.
_ A __ 153. If a line is perpendicular to two planes, the planes are parallel.
_ A __ 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.
_ A __ 155. In a plane, two lines perpendicular to the same line are parallel.
_S__ 156. In space, two lines perpendicular to the same line are parallel.
_ A __ 157. If a line is perpendicular to a plane, it is perpendicular to every line in the plane.
_S__ 158. If a line is perpendicular to a line in a plane, it is perpendicular to the plane.
_S__ 159. Two lines perpendicular to the same line are parallel.
_ A __ 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
F
Prove: AD  EC
E
D
A
169. Given:  ACE is isosceles with base CE
B, D, F are midpoints
B
F
Prove:  ABD   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
G
H
O
R
172. Given: Diagram as shown
1  4
1
I
T
2
3
C
S
4
Prove:  2   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
Prove:  WRS is isosceles
R
P
174. Given: PR  ST
NP  VT
P  T
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