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Geometry Study Guide for 1st Semester Final
Name:_________________________________________________Per_____________Date_____________
For the following three questions: Use the
following statement: “If you are a geometry
student, then you are cool.”
7. Use the diagram shown below. If
XY  4x  8 , YZ  2x  4 , and XZ  40 , then
x?
X
1. “you are cool” represents what part of the
statement?
Z
Y
2. “If you are cool, then you are a geometry
student” represents the:
3. “you are a geometry student” represents what
part of the statement.
8. Point Y is between points X and Z on a line
segment. Find the length of XY given the
following information:
XY  3x  4; YZ  4 x  9; XZ  30
4. Write the following statement in If-Then form,
and then write its converse.
“Three points on the same line are collinear.”
5. Write the following statement in If-Then form,
and then identify the hypothesis and the
conclusion.
“Dogs like to run in the park”
6. Write the following biconditional statement as a
conditional statement and its converse.
“The radius of a circle is 4 if and only if the
diameter is 8.”
For the next four questions, Fill in the blank in
the given statement:
9. __________________ parts of congruent
triangles are congruent.
10. The measure of an ______________ angle of a
triangle is equal to the sum of the measures of
the two Remote (nonadjacent) interior angles.
11. A plane contains at least _________ noncollinear points.
12. A line contains at least ___________ points.
Page 2
Use the given information and the diagram to
answer the following four questions.
19.  ABD   CBD. Name the theorem or
postulate that justifies the stated congruence.
A
Are the given pairs of angles congruent,
complementary, supplementary, adjacent, and/or
vertical?
B
5
6
7
D
8
C
13. 8 and 6
20.  ABD   CBD. Name the theorem or
postulate that justifies the stated congruence.
14. 5 and 7
A
15. 5 and 8
B
16. 7 and 6
In the diagram q  r . Answer the following two
questions using this information.
D
C
q
8
9
7
r
21. What must be true in order for
 ABC   EDC by the AAS congruence
postulate?
E
B
C
17. Are 9 and 8 , congruent, complementary or
supplementary?
D
18. Is the sum of 9 , 8 and 7 equal to 45º,
90º, or 180º?
A
Page 3
22. Which other congruence must exist in order
for  XYZ   RSZ by the SSS congruence
postulate.
26. Can you use the following length, 5, 8, and 4 to
construct a triangle? Why?
R
Y
27. Can you use the following length, 9, 15, and 4
to construct a triangle? Why?
Z
S
X
23. Which congruence postulate/theorem can be
used to prove that the two triangles shown are
congruent?
28. Can you use the following length, 25, 11, and 33
to construct a triangle? Why?
29. Can you use the following length, 7, 12, and 19
to construct a triangle? Why?
30. List all three sides in order from smallest to
largest. (triangle not drawn to scale)
A
45º
24. Which congruence postulate/theorem can be
used to prove that the two triangles shown are
congruent?
C
65º
P
B
31. List all three angles in order from smallest to
largest. (triangle not drawn to scale)
M
Q
A
N
25. List the six ways you have learned to prove that
two lines are parallel.
13
11
C
B
23
Page 4
32. The lengths of the sides of a triangle are x, 11,
and 21. What is the possible value of x?
39. In the figure (not drawn to scale), DB bisects
mADC , mADB = x+30, and
mCDB = 3x-10. Find mADC .
A
B
33. The lengths of the sides of a triangle are x, 33,
and 41. What is the possible value of x?
C
(x+30)˚ (3x-10)˚
D
34. The lengths of the sides of a triangle are x, 3,
and 5. What is the possible value of x?
40. Classify  XYZ, by its sides.
Y
35. The perimeter of a square ABCD is 80 inches,
and CD = 4x + 12. What is the value of x?
9
9
36. The perimeter of a square EFGH is 48 inches,
and EF = 6x - 42. What is the value of x?
X
37. In the diagram, CD bisects ACB . The
measures of the two congruent angles are
2 x  7  and 4 x  9 . Find x.
41. Classify  XYZ, by its sides.
X
D
A
Z
9
7
6
B
C
Z
Y
5
42. Classify  XYZ, by its sides.
Z
38. In the diagram, YZ bisects PYX . Given that
mXYP  150  , find mZYP .
2
3
Z
X
P
150
Y
Y
3
X
Page 5
43. Classify  XYZ, by its angles.
47. Use the diagram to find the value of x.
Z
xº
30˚
120º
xº
60˚
X
Y
48. Use the diagram to find the value of x.
44. Classify  XYZ, by its angles.
xº
X
65º
60º
55˚
55˚
70˚
Z
Y
45. Classify  XYZ, by its angles.
For the following four questions, use the diagram
below. (The diagram is not drawn to scale)
b˚
j
k+5
a˚
91˚
42˚
c˚
k+2
X
49. Which angle is greater, b or c ?
50. Which angle is greater, a or c ?
47˚
Z
Y
51. Which angle is greater, a or b ?
52. Is the following statement true? Yes or No
46. Use the diagram to find the value of x.
xº
120º
a  b  c
53. Find the value of x and y in the isosceles
triangle below.
xº
50º
116º
yº
Page 6
54. In the diagram below, find mA
For the following 6 questions, use the diagram
below.
62
120
6
A
7
2
3
5
8
1
4
*
55. In the figure below, x is a whole number. What
is the smallest possible value of x ?
x
x
23
58. What type of Angles are  6 and  4.
59. What type of Angles are  7 and  5.
60. What type of Angles are  4 and  1.
56. If two angles are supplementary and the
measure of one angle is eight times the measure
of the other, what is the measure of the greater
angle? What is the measure of the smallest
angle?
57. If two angles are complementary and the
measure of one angle is four times the measure
of the other, what is the measure of the greater
angle? What is the measure of the smallest
angle?
61. What type of Angles are  8 and  2.
62. What type of Angles are  1 and  8.
63. What type of Angles are  3 and  7.
64. For which value of x are lines r and s parallel?
r
(4x+35)
(6x-15)
s
Page 7
For the following 5 questions, Use the diagram
shown below in which, R // P
75. Find the coordinates of the midpoint of a
segment with the following end points,
A(5,4), B(-3,2)
R
47
9
P
5 8
36º
76. Find the coordinates of the midpoint of a
segment with the following end points,
J(-1,-9), K(11,-5)
65. Find m8
66. Find m5
77. Fill in the reasons in the following two-column
proof:
67. Find m7
Given: NQ  MP , NQ // MP
Prove: MPN  QNP
N
Q
68. Find m4
69. Find m9
M
P
Statements
70. 1 and 2 are a linear pair. 1 and 3 are
vertical angles. If m3  62 , then m2 
71. 1 and 2 are a linear pair. 1 and 3 are
vertical angles. If m2  77 , then m1 
72. 1 and 2 are a linear pair. 1 and 3 are
vertical angles. If m3  56 , then m2 
73. Find the distance between the following two
points G (3, 0) and H (8,10).
74. Find the distance between the following two
points M (1,-3) and N (3, 5).
1. NQ  MP
Reasons
1.
NQ // MP
2. QNP  MPN
3.
NP  NP
4. MPN  QNP
2.
3.
4.
Page 8
78. Provide the reasons for the following proof.
Given: BC  CD, AB  DE
Prove: AC  CE
81. Use construction tools to construct a line
through P parallel to m. Show construction lines.
P
A
B
C
D
E
Statements
Reasons
BC  CD, AB  DE
BC  AB  CD  AB
m
BC  AB  CD  DE
BC  AB  AC , CD  DE  CE
AC  CE
82. Use construction tools to construct a line
through P perpendicular to m. Show construction
lines.
79. Copy angle B onto line x with the vertex of the
new angle at point Q.
P
m
B
83. Classify  MNO.
N
x
Q
8
80. Use construction tools to construct a line
through P perpendicular to the given line. Show
construction lines.
P
M
9
10
O
[A] Equilateral
[B] Isosceles
[C] Scalene
[D] none of these
Page 9
84. Solve for x, given that AB  BC . Is ABC
equilateral?
88. The measure of  B is _____.
[A] 89
[B] 79
[C] 99
[D] 101
85. Find the value of x.
89. Given: LMN  UVW . Complete the
statements. A. UW  _____
B. LMN  ____
53°
x°
64°
86. Find the measure of exterior angle A.
87. Which of the following could NOT be a
measure of an exterior angle?
90. If  ABC   DEF, AB = 24 feet, m  B =
43  , and m  F = 31  , which of the following
statements is false?
[A] D  A
[B] mA = 106
[C] FD = 24 ft
[D] ED = AB
91. Write a two-column proof:
Given: BD and AC bisect each other
BC  AD
BC  AD
C
Prove: BCE  DAE
B
A
40
E
65
B
[A] 105
[B] 125
[C] 115
[D] 140
C
A
D
Page 10
92. Refer to the figure below. Which of the
following statements is true?
H
95. Refer to the figure shown. Give a congruence
statement for the two triangles and name the
theorem or postulate that proves the congruence.
I
G
J
I
= JI
GJ ~
K
H
J
HI  JK
IJ  LK
[A] There are no congruent triangles.
[B] GIJ  JHG by SSS
96. Which postulate or theorem can be used to
determine the measure of
RT ?
[C] GHJ  IHJ by SAS
[D] GJH  IJH by SSS
93. State the postulate or theorem that can be used
to conclude
that OCD  OAB .
[A] SSS Congruence Postulate
[B] AAS Congruence Theorem
[C] ASA Congruence Postulate
94. Refer to the figure shown. Which of the
following statements is true?
U
V
W
T
TV  WV
UV  XV
X
[A] TUV  WXV by SAS
[B] TUV  VWX by SAS
[C] TUV  XWV by ASA
[D] TUV  WXV by ASA
[D] SAS Congruence Postulate
97. Given: B  E and C  F . What other
piece of information is needed to show
ABC  DEF by ASA Congruence Postulate?
[A] A  D
[B] EF  FE
[C] B = F
[D] BC  EF
L
Page 11
98. Given:  DCA   BCA, B  D
Prove: AB  AD
B
C
104. Write an indirect proof.
Given: m  1 = 122  and m  2 = 121 
Prove: a || b
a
1
A
2
b
D
99. Given the points P(–1, –6), Q(15, 24), and
M(7, 9), prove that M is the midpoint of PQ.
100. Refer to the figure below.
105. What is the sum of the measures of the exterior
angles of any polygon?
106. Find the measure of the missing angle.
?
A. If BC = 15, then LN = ______.
B. If AB = 3x + 5 and NM = 2x + 1, then NM =
______.
101. The coordinates of the midpoints of the sides
of a triangle are L(0, 1), M(4, 0), and N(2, –2). Find
the coordinates of the vertices of the triangle.
72°
116°
108°
107. Find x and y.
131°
x°
102. Two sides of a triangle have lengths 8 and 11.
What are the possible lengths of the third side x?
103. Two sides of a triangle have lengths 7 and 13.
The third side, x, has a length that is ______.
[A] 6 < x < 13
[B] < 6
[C] > 20
[D] 6 < x < 20
119° y°
56°
Page 12
108. Find AM in the parallelogram if PN  6 and
MO  18.
M
111. For parallelogram PQLM below, if
mPML  83 , then mMLQ  ______ .
N
A
P
O
[A] 83
[B] mQLM
[C] 97
[D] mPQM
109. Refer to the figure below.
U
V
15
29°
24
Y
17°
X
41
W
Given: UVWX is a parallelogram, mWXV  17 ,
mWVX  29 , XW  41, UX  24 , UY = 15
A. Find m  WVU.
B. Find WV.
C. Find m  XUV.
D. Find UW.
112. Consecutive angles in a parallelogram are
ALWAYS ________.
[A] vertical angles
[B] complementary angles
[C] supplementary angles
[D] congruent angles
113. Choose the statement that is NOT ALWAYS
true.
For any parallelogram _______.
110. For parallelogram PQLM below, if
mPML  83 , then mPQL  ______ .
[A] opposite sides are congruent
[B] the diagonals are perpendicular
[C] the diagonals bisect each other
[D] opposite angles are congruent
[A] 97
[B] 83
[C] mQLM
[D] mPQM
Page 13
114. If ON  8 x  6, LM  5x  3, NM  x  5, and
OL  5 y  7, find the values of x and y given that
LMNO is a parallelogram.
O
118. Use the distance formula to determine whether
ABCD below is a parallelogram.
N
L
M
1
3
[B] x = 3; y 
1
3
[C] x = 3; y 3
[D] x = 1; y 
11
5
[A] x = 1; y 
115. Given: ABF  DEC and FB || EC
Prove: BCEF is a parallelogram
F
E
D
119. Choose the statement that is NOT always true.
For an isosceles trapezoid _______.
[A] the diagonals are perpendicular
[B] the legs are congruent
[C] the diagonals are congruent
[D] the base angles are congruent
120. For the isosceles trapezoid shown below, the
B & C are _______.
A
B
C
A
B
116. (2, 3) and (3, 1) are opposite vertices in a
parallelogram. If (0, 0) is the third vertex, then the
fourth vertex is _____.
5 
[A]  , 2 
2 
[C] 5, 4
D
[B]  1, 2
[D] 1,  1
117. If the diagonals of a parallelogram are
perpendicular, then the parallelogram is also what
type of figure?
C
[A] Congruent
[B] perpendicular
[C] Supplementary
[D] Complementary
121. Use slope and/or the Distance Formula to
determine the most precise name for the figure: A(–
8, –7), B(–3, –3), C(1, 2), D(–4, –2).
[A] rectangle
[B] rhombus
[C] kite
[D] square
Page 14
122. Describe the figure using as many of these
words as possible: rectangle, trapezoid, square,
quadrilateral, parallelogram, rhombus.
123. Describe the figure using as many of these
words as possible: rectangle, trapezoid, square,
quadrilateral, isosceles trapezoid, parallelogram,
rhombus.
127. Given: AC  BD If AC = 18 and BD = 15, find
the area of kite ABCD.
128. The area of the quadrilateral is
_____.
[A] 58 sq. units
[B] 23.3 sq. units
[C] 16.25 sq. units
[D] 380 sq. units
129. An expression for the area of kite ABCD is
_____.
124. Find the area of a square with side length 15
m.
125. The area of the parallelogram is _____.
[A] 40 111 sq. units
[B] 340 sq. units
[C] 800 sq. units
[D] 680 sq. units
126. In rhombus ABCD, AB = 20 and AC = 32.
Find the area of the rhombus to the nearest tenth.
[A] 379.3
[B] 384.0
[C] 506.0
[D] 499.6
[A]
( BD)( AC )
2
[B] (AC)(BD)
[C]
( AB)  (CD)
( BD)
2
[D] (AB)(AD)