Download GEOMETRY: END OF YEAR REVIEW

GEOMETRY: EXAM (A)
1.
Name:_______________________
How many non collinear points determine a plane?
10. If mA = 127 and mB = 53, then they are:
A) none
2.
D) three
B) 12
C) 18
D) 24
Name the intersection of planes BCQ and CDS in the
figure below.
B
C
E
A
Q
P
4.
C) two
How many edges does a hexagonal prism have?
A) 6
3.
B) one
D
A) CR
B) D
C) C
D) BC
A)
complementary angles
B)
supplementary angles
C)
vertical angles
D)
interior angles
11. Given the statement: “If it is raining, then I will stay
inside.” Identify the hypothesis.
A)
I will stay inside.
B)
I will not stay inside.
C)
It is raining.
D)
None of these.
R
T
S
What is the distance between (-4, -3) and (5, -7)?
A) √15
B) √17
C) √65
D) √97
12. If C lies in the interior of ABG, then mABG is equal to:
{hint: draw a diagram}
5.
Which term below is not one of the three undefined terms?
A) line
6.
B) point
D) ray
An eight – sided polygon is a (n):
A) pentagon
7.
C) plane
B) hexagon
C) octagon
D) decagon
A)
mABC − mCBG
B)
c)
mAGB + mCBG
mABC + mCBG
D) mCBG − mABC
13. Coplanar lines which do not intersect are called:
Rewrite the statement below in “if . . . then” form.
A) parallel lines
B) skew lines
C) acute lines
D) obtuse lines
“ All squares are rectangles.”
8.
A)
If a figure is a square, then it is a rectangle.
B)
If a figure is a rectangle, then it is a square.
C)
If a figure is not a rectangle, then it is not a square.
D)
If a figure is not a square, then it is not a rectangle.
Name a segment congruent to BE using the number line
below.
A) CG
A and B are complementary. If mA = 4x + 6 and
mB = 3x, find mA.
A) 90
9.
14.
B) 12
C) 54
C
B
D
E
C) BF
D) CH
A
B
C
D E
F
G H
-5
-4
-3
-2
0
1
-1
2
15. State the inverse of the following statement.
“If x is not even, then x + 1 is not odd.”
D) 36
mABD = 5x + 9 and mCBE = 7x – 5. Find mCBE.
A
B) AD
A) 84
B) 7
C) 44
D) 19
A)
If x + 1 is odd, then x is even.
B)
If x + 1 is not odd, then x is not even.
C)
If x is even, then x + 1 is odd.
D)
None of these.
16. What is the interior angle sum of a decagon?
A) 360
B) 1800
C) 144
22. If mABC = 47 and mCBD = 18, find mABD.
D) 1440
A
C
B
D
A)
65
B)
19
C)
45
D)
29
17. Given DB  BC. Classify ABC.
D
A
C
23.
A
B
A) acute
If BD bisects ABC, what is the measure of ADB?
B
100
B) right
C) obtuse
35
A) 35
B) 45
C) 60
D) 70
D) straight
D
18. A point P is picked at random on AF. What is the
probability that P is on BD?
A
B
C
D E
F
G
-3
-2
-1
0
2
3
A) 0
B)
1
5
1
C)
2
5
C
USE THIS PICTURE FOR 24-25.
D) 1
1
2
3
k
4
5
19. The coordinate of A is 13 and the coordinate of the
midpoint M of AB is –15. Find the coordinate of B.
6
7
8
j
24. Choose the correct name for angles 4 and 5.
A) -43
B) 43
C) -2
D) 28
A) vertical angles
B) alternate exterior angles
C) corresponding angles
D) alternate interior angles
20. Given the statement: “If three lines have a point in common,
then they are coplanar.” Identify the converse.
A)
B)
C)
D)
If three lines are not coplanar, then they do not have a
point in common.
If three lines are not coplanar, then they have a point
in common.
If three lines are coplanar, then they have a point in
common.
If three lines are coplanar, then they do not have a
point in common.
21. A convex polygon whose sum of the interior angles
measure 720 is a (n):
A) pentagon
B) hexagon
C) octagon
D) decagon
25. Given k and j are parallel. Find the corresponding angle
to 7.
A) 1
B) 3
C) 5
D) 6
26. In isosceles trapezoid PQRS, PS  RQ. If mP = x then
mS = ______.
A) 180 – x
B) x
C) x – 180
D) 90-x
27. The legs of a 45 – 45 – 90 triangle are five inches long.
Find the length of the hypotenuse.
A) 5√3 in.
B) 10 in.
C) 5√2 in.
D) √5 in.
28. To solve for x in ABC below, which equation should be
used?
C
x
31
A
A)
sin 31 =
10
𝑥
10
B)
cos 31 =
10
𝑥
C)
tan 31 =
𝑥
10
D)
sin 31 =
10
𝑥
B
B
2
A
B) 40√2
C) 40
30. ABCD is a trapezoid with median
x–5
A
C
1
D) 15
B) 10
C) 17
D) 34
B
A
T
2
B
R
A) x = 8
B) x = 18
C) x = 6
D) x = 12
x
D
C
What is the length of
S
34. If AB  CD, find x.
F
2x – 1
D) 65
Q
9
D
C) 55
P
A) 5
3
E
B) 45
33. In parallelogram PQRS, PT = 5x – 8 and RT = 3x + 2.
Find PR.
EF .
12
A) 35
D
29. ABC is a 30 – 60 – 90 triangle. If the side opposite the
30 angle is 20, find the length of the side opposite the 60
angle.
A) 20√3
32. Quadrilateral ABCD is a rhombus. If m1 = 35, then
m2 = ________.
C
AB ?
35. State the congruence method that can be used to prove the
triangles below congruent.
A)
5
B)
7
A)
AAS
C)
9
B)
ASA
D)
10
C)
SSS
D)
HL
31. What type of triangle is ABC?
C
x + 15
A
2x - 10
4x - 20
B
A) scalene
B) isosceles
C) equilateral
D) right
36. Find the volume of a chocolate cake if the height is 6
inches and the diameter is 8 inches.
A) 60.24 in3
B) 301.59 in3
C) 603.19 in3
D) 1205.76 in3
37. If EAY  SAY, which additional congruent,
corresponding parts are needed to prove EAY  SAY by
SAS?
A)
̅̅
̅̅̅̅
𝐸𝑌 ≅ ̅̅
𝑆𝑌
B)
E  S
C)
̅̅̅̅ ≅ ̅̅̅̅
𝐸𝐴
𝑆𝐴
D)
EYA  SYA
B
E
D
A
38. Find the area of an isosceles trapezoid whose vertices have
coordinates (-2, -1), (1, 1), (4, 1), and (7, -1).
A) 24
43. Given that point D is the midpoint of AB and point E is the
midpoint of BC. Find AC if DE = 14.
B) 12
C) 18
C
A)
7
B)
10
C)
20
D)
28
44. ∆ABC is equilateral. Find the measure of arc AB in the
figure.
D) 6√13
39. Which of the following is a chord?
A)
120
B)
60
C)
30
D)
15
A
A)
AC
B
F
B)
BD
C)
EF
D)
BD
E
G
C
45. In circle O, AB is a diameter, mAC = 100. Find mD.
D
C
40. Find the measure of x in the figure below.
A)
15.39
B)
8.39
C)
5.44
D)
18.36
O•
A
D
B
A)
20
B)
90
C)
50
D)
10
46. BC and BA are tangents to circle O. If BC = 12 and the
radius of circle O is 5, then find the length of OB.
A) 7
B) 13
C) 17
D) 60
41. Given mB = 20, mCAB = 102. Find mBCD.
B
C
A
A) 122
B) 20
A
D
C
C) 102
B
D) 82
47. Which picture shows a triangle inscribed in a circle?
42. RT is a diameter of circle O and m RS = 128. Find mR.
S
A)
64
B)
52
C)
26
D)
128
R
O
T
A
B
A) picture A
B) picture B
C) picture C
D) none of these
C
48. The area of a circle is 36. What is its circumference?
A) 6
B) 12
C) 18
54. One difference between a rhombus and a square is:
D) 72
49. ABC is translated by (x, y)  (x + 3, y – 2). If the
coordinates of the triangle are A(0, 0), B(-5, 7) and C(2, 3),
what are the coordinates of B’?
A)
(-8, 9)
B)
(-2, 5)
C)
(3, -2)
D)
(5, 1)
A)
A square has four right angles, a rhombus does not
necessarily.
B)
A square has four congruent sides, a rhombus does
not necessarily.
C)
A rhombus has congruent sides and congruent angles,
a square does not.
D)
There are no differences between a square and a
rhombus.
55. In the figure below, if ABCD is a parallelogram, what are
the coordinates of vertex D?
50. Given circles A and B are tangent. The length of AB is __?
A
B
•
•
A)
(10, -1)
B)
(7, -1)
C)
(6, -1)
D)
(4, -1)
B (3,10)
D
A (-1,-1)
3
4
56. What is the length of arc AB?
A) 7
B) 14
C) 5
D) 12
A)
A
4√2
4
B) 2
B
O
51. If AB and AC are tangent segments, and AB = 6, what can
be concluded about ̅̅̅̅̅
𝐴𝐶 ?
B
C (8,10)
A
C
C) 4
D) 15
A)
cannot determine
length of AC.
B)
AC = 3
C)
AC = 6
A) always
D)
AC = 3√2
B) sometimes
57. A rectangle is __________ a square.
C) never
58. Find the volume of the cylinder below.
52. Given mAEB = 30 and the measure of arc AB is 80,
find the measure of arc CD.
A)
10
B)
20
C)
25
D)
40
A
C
E
D
B
A)
45 π units3
B)
94 π units3
C)
30 π units3
D)
15 π units3
3
5
59. Reflect the following points over the x-axis:
P(-2, 4) and Q(1, 4).
53. If CD = DE then AD is a _____ of ACE.
A
A) centroid
B)
median
C)
altitude
D)
hypotenuse
C
D
E
A)
 2  1
4
4 

B)
 2 1 
  4  4


C)
2 .1 
 4  4


D)
 4  4
 2 1 


66. DOG is rotated 90 counterclockwise about the origin.
What are the new coordinates of D?
60. Find the area of the trapezoid below.
A)
210 units2
B)
175 units2
C)
90 units2
D)
15
16
8
6
A) (-3, 0)
O
B) (0, -3)
105 units2
D
20
C) (3, 0)
G
D) (0, 3)
61. Find the lateral area of the right prism.
A)
94
B)
70
C)
35
D)
60
5
67. In isosceles PQR, P is the vertex angle. If
mQ = 8x – 3 and mR = 2x + 15, find the measure of
P.
3
A) 3
4
62. In the figure on the right, name one additional
pair of corresponding parts that needs to be congruent in order
to prove that STP  MKO by AAS.
K
A) S  M
B) TP  KO
T
C) T  K
M
D) ST  MK
S
O
P
63. Find the area of a sector of a circle with an arc measure of
45 and with a radius of 4.
A) 16
B) 8
C) 2
D) 2
64. If a point is chosen at random in the interior of circle O,
what is the probability that the point is in the interior of
AOB?
A
A)
C)
2
𝜋
B)
1
4
D)
5
2𝜋
4
O
B
1
2𝜋
65. In isosceles PQR, P is the vertex angle.
If mQ = 8x – 33 and mR = 2x + 15, find the measure of P.
A)
8
B)
31
C)
62
D)
118
B) 21
C) 42
D) 138
68. What is the value of x in the diagram?
A)
4 37
B)
20
x
16
C)
777
D)
4 21
21
69. What is the largest angle in the figure below?
A)
V
B)
W
C)
Y
D)
Z
W
7
12
9
X
6
Y
8
10
V
Z
70. If the degree measures of the angles of a triangle are in
ratio 2:3:4. What is the measure of the largest angle?
A) 20
B) 40
C) 80
D) 90.
71. Which could not be the lengths of the sides of a triangle?
A) {1, 4, 4}
B) {1, 11, 12}
C) {3,5,7}
D) {8, 11, 18}
72.
In the figure, what is the value of y?
78. The perimeter of rectangle JKLM is 36. Find the area.
A) 40
A) 10
B) 40
C) 80
D) 224
J
8
M
B) 50
C) 80
K
L
D) 60
73. Find the image of ACE with vertices A (7, 2), C (-8, 5),
E (0,-6); translation: 〈−9 , 4 〉.
79. BD is the angle bisector of ABC, mABD = 3x + 2, and
mDBC = 4x – 6. Find mABC.
A
D
B
A) A’ (11, -7), C’ (-4, -4), E’ (4, -15)
B)
A’ (-2, 6), C’ (-17, 9), E’ (-9, -2)
C)
A’ (-63, 8), C’ (72, 20), E’ (0, -24)
D)
A’ (-2, 8), C’ (-17, 9), E’ (0, -2)
A) 8
80. In RST, m<R = x + 10, m<S = x + 5, m<T =
3x – 35 . List the sides in decreasing order.
74. What is the volume of a regular square pyramid with
base edge 16 and height 6?
A) 1536
B) 512
C) 256
D) 128
C
B) 24 C) 26 D) 52
̅̅̅̅
̅̅̅ , ̅̅̅̅
𝑅𝑆, ̅𝑆𝑇
𝑇𝑅
̅̅̅̅
̅̅̅
̅̅̅̅
𝑇𝑅 , 𝑅𝑆, ̅𝑆𝑇
A.
C.
̅𝑆𝑇
̅̅̅, ̅̅̅̅
𝑅𝑆, ̅̅̅̅
𝑇𝑅
̅𝑆𝑇
̅̅̅ , ̅̅̅̅
𝑇𝑅 , ̅̅̅̅
𝑅𝑆
B.
D.
81. Quad ABCD  Quad HGFE. What is the scale
factor?
A. 3:1
75. Find x if the surface area of the figure is 286
A
B. 21:6
in2.
A) 14 in.
B) 8 in.
C. 1:3
12
C) 7 in.
D) 6 in.
D. 4:1
B
x
5 in.
9 in.
76.
Find the area of the shaded region.
A)
144 – 36 π

B) 144 + 36 π
C)
144 – 144 π
D)
96 – 144 π
12 cm
21
H
E
D
4
3
F
C
G
6
82. In the diagram shown below, 𝑙 // 𝑚 , m2 = (4x – 2)º and
m8 = (3x – 21)º. What is the measure of 5?
A)
24
B)
66
C)
29
D)
114
3
5
7
l
1 2
4
6
m
8
83. What additional information would be needed to prove
ABD  CDB by AAS ?
12 cm
77. The perimeter of an equilateral  is 30. Find the area.
A)
25 3
B) 50
C)
50 3
D) 100
A)
ABD  CBD
B)
̅̅̅̅ ≅ ̅̅̅̅
𝐴𝐷
𝐶𝐵
C)
DAB  BCD
D) ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷
A
D
B
C
84. The mast of a sailboat is a right triangle. Find the height
of the mast.
A)
4
√41
D)
5.1
of side EF ?
E
3x + 6
8.2
G
B) 21
C). The diagonals are perpendicular to each other.
C) 19
D). The opposite angles are congruent.
D) 7
89.
A) 150 in2
A cone has a radius of 12 cm and a height of 9
cm. What is the approximate lateral surface
area?
A) 89 cm2
B) 140.5 in2
B) 123 cm2
60°
C) 424 cm2
D) 129.9 in2
87.
2x + 5
A) 27
B). The consecutive sides are congruent.
The lengths of two consecutive sides of a
parallelogram are 10 inches and 15 inches. The
two sides also form a 60° angle. Find the area
of the parallelogram.
27
H
A). The diagonals are congruent.
C) 139.4 in2
F
5
85. Which statement is true about ALL parallelograms?
86.
Given parallelogram EFGH, what is the length
h
B) 3.2
C)
88.
A 20 ft ladder is leaning against a wall. The
foot of the ladder is 7 ft from the base of the
wall. What is the approximate measure of the
angle the ladder forms with the ground?
D) 565 cm2
90.
The exterior angle of a base angle in an
isosceles triangle is 100°. What is the measure
of the vertex angle?
A) 70.7°
A)
20°
B) 69.5°
B)
40°
C) 20.5°
C)
60°
D) 19.3°
D) 80°
END OF EXAM:
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