Part I: Determine whether each statement is true (T) or false (F).
T F 1. Some circles have a radius of 1.
T F 2. If the scale factor of one triangle to another is 1:4, then the ratios of the areas is 1:16.
T F 3. If the measure of one acute angle of a right triangle is 30°, then the measure of the other acute angle is 60°.
T F 4. If the legs of a right triangle are congruent, each acute angle has a measure of 45°.
T F 5. The hypotenuse of a 45°-45°-90° triangle is 2 times as long as a leg.
T F 6. A dodecagon has twenty sides.
T F 7. When a central angle and an inscribed angle intercept the same arc, the two angles are congruent.
T F 8. A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
T F 9. The measure of each interior angle of a regular hexagon is 120°.
T F 10. An angle inscribed in a semicircle is a right angle.
T F 11. If two circles are congruent, then their diameters are congruent.
T F 12. If a diameter is perpendicular to a chord, then it bisects the chord.
T F 13. A circle with an area of 121  units 2 has a circumference of 11  units.
T F 14. All angles which intercept congruent arcs of a circle are congruent.
T F 15. The central angle of a regular decagon is 36°.
T F 16. The sine ratio is defined to be the ratio of the length of the adjacent leg to the length of the hypotenuse.
T F 17. The area of a right triangle with side lengths of 3, 4, and 5 is 6 units.
T F 18. Opposite angles of an inscribed quadrilateral are complementary.
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Part II: Determine whether each statement is ALWAYS (A), SOMETIMES (S), or NEVER (N) true.
19. A radius of a circle is ___________ a chord of the circle.
20. The diagonals of a quadrilateral are ___________ perpendicular.
21. The bases of a trapezoid are ___________ parallel.
22. “Proven” is ___________ a reason in a proof.
23. The exterior angles in a triangle _____________ add up to 360°.
Part III: Multiple Choice. Choose the BEST answer and place it in the space provided.
____ 24. Which of the following is not an isometry?
a. translation b. rotation c. reflection d. dilation
____ 25. If the length of the shorter leg of a 30°-60°-90° triangle is 4, then the length of the
hypotenuse is
a. 2 b. 4 3 c. 4 2
For 26 and 27, use the diagram to the right.
____ 26. If AD = 3 and DB = 27, find CD.
d. 8
a. 6 2 c. 40.5
b. 9 d. 81
____ 27. If BC = 15 and BD = 10, find AD.
c. 22.5 a. 6.66
b. 12.5 d. 125
____ 28. Find the perimeter of a square whose area is 36.
a. 6 b. 12 c. 24 d. 36
the length of NO is
a. 5 2 c. 10
b. 5 3 d. 10 3
B
M
N
10
30

D
C
O
A
2

____ 30. If the perimeter of a square equals 20 2, the length of each diagonal of the square is
a. 10 2 b. 5 2 c. 10 d. 5
____ 31. If the sides of a triangle are 3, 4, and 6, then the triangle is
a. a 30°-60°-90° triangle c. a 45°-45°-90° triangle
b. an acute triangle d. not a right triangle
____ 32. If the length of the hypotenuse of a 45°-45°-90° triangle is 8, then the length of a leg is
a. 8 2 b. 4 2 c. 4 d. 4 3
For 33 and 34, use the diagram to the right.
if m S 90 , then tan R =
a.
TS RS TS
RS
b.
TS
c.
RT
if m S 90 , then sin T =
d.
RS
RT
R
a.
TS
a. X
b.
RS
c. W diagonal of the rhombus.
a. 10 cm b. 5 cm
c.
RS
RT TS RT RS
____ 35. A rhombus has a diagonal of 24 cm and an area of 120 cm 2 . Find the length of the other
c. 13 cm
d.
____ 36. What is the reflection image of V over line
b. Y d. T
For 37 and 38, use circle R to the right.
____ 37. A major arc of circle R is
RT
d. 12 cm
?
U
T
S
V
G b
X
D
T
Y
a. DEF b. EF c. DGF d. ED E
 R
a. mDEF b. mGDE c. mGFD d. mGDF
F
3
W

For 39 – 41, use circle O to the right.
____ 39. The measure of ABC
a. 100° b. 90°

c. 80°
____ 40. The measure of A
a. 40° b. 50°

c. 60°
d. 70°
d. 70°
a. 85° b. 95°

c. 55° d. 100°
   and
100

A
B mXW 105 , then mXY 
a. 95° b. 100° c. 105° d. 110°
____ 43. Find the area of a circle whose circumference is 10  .
a. 5  b. 20  c. 25 
For 44 and 45, use circle S to the right.
d. 100 
____ 44. If mFG 80  and mEC 44 , then m D
a. 62° b. 38° c. 22° d. 18°
____ 45. If CX = 12, XG = 2, and XH = 3, then XF =
a. 12
D
E
b. 8 c. 4.5 d. 2
____ 46. The length of a diagonal of a square is 6. The length of each side is
a. 6 2 b. 3 2 c. 6 d. 3
X
C
4
Y
110

O
X
S
P
C
F
D
X
H
G
W
Z

For 47 and 48, use the diagram to the right.
____ 47. If AD = 2.5, and AB = 10, find BC.
C
a. 6 b. 8 c. 5 3 d. 8 3
____ 48. If AD = 7 and AB = 28, find AC.
a. 14 b. 21 c. 4
c. X = 6, y = 40, z = 6
d. x = 41, y = 40, z = 6
d. 28
____ 49. The transformation to the right is an isometry.
What are the value of the variables?
a. x = 41, y = 6, z = 6
b. x = 40, y = 6, z = 9
____ 50. How many lines of symmetry does polygon
a. 0 b. 1 c. 2
A
d. 5
D
A
101

(8y - 6)

to have?
D
B
18
C
5
3z
L
K
42

(2x + 19)

M
J
B

Part IV: Matching. Match each figure with its area.
SET 1
____ 51.
____ 53.
____ 55.
5
8
12
21
11
7
8
6
6
____ 52.
____ 54.
8
5
SET 2
____ 56.
4
3
3
4
____ 57.
____ 58.
13
10
____ 60.
4
30

5
____ 59.
2
10
3
3
12
10
13
9
6
6
A. 128
B. 28
C. 50
D. 64
E. 72
A. 30
B. 24
C. 25
D. 2 3
E. 33

Part V: Matching. Match each part to its correct name. BE SPECIFIC!!
C
B 2
A
1
D
O
H
E
F
G
A. chord ____ 61. CG
____ 62. DE
____ 63. D
____ 64. AB
____ 65. HF
B. secant
C. diameter
D. point of tangency
E. tangent
AB. inscribed angle


____ 69. OD
AC. central angle
AD. radius
AE. right angle
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Part VI: Select the best answer from the list.
____ 70. Find x. x y
6
____ 71. Find y.
____ 72. Find a.
____ 73. Find b.
____ 74. Find e.
____ 75. Find f. a e
40 b
18 f
30

30
8
A. 12 3
B. 48.6°
C. 6 2
D. 6 3
E. 6
F. 41.4°

Part VII: Free Response. Solve for the indicated values. Show all work. Round answers to the nearest tenth, when appropriate.
76. Find x and y.
108
 y x
124

65

77. A quadrilateral has the vertices A(0, 3), B(6, 6), C(0, 6), and D(–3, 3). Graph the image after a dilation with a scale factor of
1
3
.
78. Graph the given circle: (x – 1) 2 + (y + 3) 2 = 4
79. Find the area of this right triangle if b = 17 and c = 514. c b
80. A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse triangle. Explain. a
9

81. Find the exact values of x and y. (No decimals!)
82. Find the value of x, to the nearest whole number. (not drawn to scale)
D
F
53

4
30
 x y x
E
14
83. Find mPQ in circle A. Drawing is not to scale.
(Diagram is not drawn to scale.)
B
A
(2y - 15)

P
A
Q
S
(y + 35)

R
84. What must be the measures of B  so that a circle can circumscribed about ABCD?
103

C
78

D
85. Find the value of x if mAB 41    (not drawn to scale)
A
10
B x
O
D
C

86. Find the sum of the measures of the interior angles of a decagon.
87. Find the number of sides of a regular polygon with each interior angle equal to 150°.
88. Find the measure of an interior and an exterior angle of a regular polygon with 15 sides.
89. Find the volume of the cylinder.
4 m
7 m
90. Find the lateral area of the rectangular prism.
6 in.
10 in.
8 in.
91. Find the total surface area of the cone.
16 cm
20 cm
12 cm
92. Find the volume of the pyramid. 15 m
16 m
17 m
16 m
11

93. Find the surface area AND the volume of the sphere.
9
94. An 8 foot ladder is leaning against a house and makes a 48° angle with the ground. How far is the foot of the ladder from the house?
95. What is the area of a circle whose circumference is 16  ?
96. What is the area of a square whose perimeter is 24 units?
97. Identify the center and radius of the given circle: x 2 + (y + 6) 2 = 49
98. Write the equation of a circle whose center is (3, –3) and has a point on the circle at (3, –9).
99. If the legs of a right triangle have the measures 5 and 8, what is the length of the hypotenuse?
12