Geometry 2nd Semester Final Review
Name
Period
Chapter 6
1.
Which of the following does NOT represent a polygon?
I.
A.
B.
C.
D.
E.
2.
4.
III.
IV.
V.
I, II, and IV only
I and II only
II, III, and V only
III and V only
II and IV only
Which term below best describes the polygon?
A.
B.
C.
D.
3.
II.
Equilateral
Equiangular
Regular
None of the above
Which term(s) below best describe the polygon?
I.
III.
Equilateral
Convex
A.
B.
C.
D.
I and III
I and IV
I, II, and IV
IV only
II.
IV.
Equiangular
Concave
Which of the following show a concave hexagon?
I.
A.
B.
C.
D.
E.
II.
I and II only
III and VI only
V only
IV only
III, V, and VI only
III.
IV.
V.
VI.
Page 2
5.
Find the value of x.
A.
B.
C.
D.
6.
If MATH is a parallelogram, then which of the following must be true?
A.
B.
C.
D.
7.
M
M ≅ H
MA ≅ HM
MA ≅ AT
m A + m T = 180°
A
H
T
In Rhombus WXYZ find x.
A.
B.
8.
x°
69
74
125
291
X
W
4(x + 2)°
10
22
(3x + 18)°
3
C.
93
D.
E.
96
122
7
Z
Y
H
C
CHEV is a parallelogram. If HY = 2(2x + 3), CY = 10,
and VY = 18, what is the value of x?
2(2x + 3)
10
A.
B.
C.
D.
3
3.75
5.25
6
Y
18
E
V
9.
MATH is a rhombus. What are the values of x and y?
M
A.
B.
C.
D.
x = 6, y = 3
x = 6, y = 4
x = 3, y = 3
x = 3, y = 6
13
H
10.
A
y+7
4x + 1
T
Quad. ZOID is an isosceles trapezoid with
ZO || ID. Find the value of x.
A.
B.
C.
D.
21
27
51
69
Z
(2x)°
D
O
(x + 27)°
I
Page 3
11.
The lengths of the bases of a trapezoid are 14" and 20".
What is the length of the midsegment of the trapezoid?
A.
B.
C.
D.
20 in.
17"
18"
20"
34"
x
14 in.
12.
What is the area of the parallelogram?
A.
B.
C.
D.
E.
13.
225 cm2
255 cm2
330 cm2
450 cm2
510 cm2
17 cm
30 cm
Find the area of ∆CAT
A.
B.
C.
D.
15 cm
10
C
2
120 u
125 u2
204 u2
238 u2
T
24
A
14.
Find the area of the trapezoid.
A.
B.
C.
D.
544 square units
448 square units
272 square units
224 square units
10
22
14
17
K
15.
Find the area of the kite.
A.
B.
C.
D.
72
117
176
352
9
E
8
8
13
T
I
Page 4
Chapter 8
16.
If
3
x −5
A.
B.
C.
4x
, then
x=3
x = –1
x = –7
7
x=
3
D.
17.
7
=
Which triangle is not similar to any of the others?
A.
B.
C.
60
D.
o
80o
60o
30o
30o
50o
18.
Which of the following could be used to prove that ∆REX ∼ ∆JOB.
A.
B.
C.
D.
J
R
AA Similarity
SAS Similarity
SSS Similarity
The triangles are not similar
9
30
X
E
12
B
19.
O
40
The triangles are similar. Find x.
x
A.
B.
C.
D.
11
16
20
44
22
6
12
20.
Find x.
A
A.
B.
C.
D.
4
8
9
11
15
D
x
10
F
6
E
C
B
Page 5
21.
The triangles are similar. Find x.
A.
B.
C.
D.
3
4
5
6
x+1
9
10
15
22.
Find x.
A.
B.
C.
D.
E.
23.
9
15
20
45
60
77°
15
4
39°
3
A.
B.
C.
D.
8
10
13
25
20
x
25
In which transformation is the image not congruent to the original figure?
A.
B.
C.
D.
25.
77°
Find x.
8
24.
39°
x
dilation
reflection
rotation
translation
Which dashed figure represents a dilation of the
given quadrilateral?
I
A. I
B. II
C. III
II
III
Page 6
Chapter 9
26.
A 15 foot utility pole must be anchored by a wire 8 feet from its base. How long is the wire from
the top of the pole to the ground?
A.
B.
C.
D.
17 feet
20 feet
161 feet
25 feet
x
15 ft
8 ft
27.
A 13 foot ladder leans against a wall so that the base of the ladder is 5 feet from the wall. How
high up on the wall will the ladder reach?
A.
B.
C.
D.
8 feet
12 feet
194 feet
15 feet
13 ft
x
5 ft
28.
Choose the sets that could be the side lengths of a right triangle.
I.
III
A.
B.
C.
D.
29.
II.
IV.
3, 4, 5
5, 12, 13
II only
II and IV
I, II, IV
I, II, III, IV
What is the length of AC in the triangle below?
A.
B.
C.
D.
30.
1, 2, 5
6, 8, 11
5
5 2
5 3
10
A
45°
5
45°
B
5
C
What is the value of x in the triangle below?
A.
B.
C.
D.
7
7 2
14
14 2
x
45°
x
14 2
45°
Page 7
31.
Which of the following can be the length of the sides of a 30°-60°-90° triangle?
I.
A.
B.
C.
D.
E.
32.
33.
5, 10, 5 3
II. 2, 2, 2 3
III. 3, 6, 3 3
I only
II only
III only
I and III only
I, II, and III
Find the value of x.
A.
4
B.
4 3
C.
4 2
D.
6
60o
8
x
30o
The shadow of a monument is 50 feet long when the sun makes a 60o angle of elevation with level
ground. What is the height of the monument?
A.
B
C.
D.
50 ft
50 2 ft
50 3 ft
100 ft
60o
50 ft
34.
Find the value of x.
A.
B.
C.
D.
35.
5
5 3
10
10 3
D
x
30°
O
5 3
Using ∆ABC, give the ratio for sin C.
A.
B.
C.
D.
8
6
4
3
4
5
3
5
A
8
B
10
6
C
G
Page 8
36.
Find tan D.
A.
.
B.
C.
D.
37.
B.
C.
D.
D
8
4
F
x
10
10
sin 34° =
x
x
cos 34° =
10
x
tan 34° =
10
sin 34° =
34o
10
x
Find the equation that will find the height of the air balloon.
A.
B.
C.
D.
39.
E
4 5
Which equation can be used to find the value of x in the triangle?
A.
38.
5
5
1
2
2 5
5
2
h
75
75
tan51o =
h
75
cos51o =
h
h
sin51o =
75
tan51o =
h
51o
75 ft
Which equation could you use to find the value of x?
B.
tan 42
10
x = 10(tan 42)
C.
x =
A.
x =
D.
10
tan 42
x = 10(cos 42)
E.
x =
10
cos 42
42°
x
10
Page 9
Chapter 10
40.
Which figure represents a chord of circle P?
A.
B.
C.
D.
PM
MN
PS
TS
M
O
N
P
S
Q
41.
42.
Which figure represents a tangent of the circle?
A.
B.
OT
MN
C.
QS
D.
PM
T
Find the value of x.
x°
A.
B.
C.
D.
43.
o
30
45o
60o
90o
.
If m∠OWL = 70°, find m OL
A.
B.
C.
D.
70°
110°
140°
220°
P
L
O
70°
W
44.
Use the diagram to find the measure of ∠ x.
184°
A.
B.
C.
D.
54°
58°
122°
126°
x°
68°
Page 10
45.
Use the diagram to find m∠x.
A.
B.
C.
D.
46.
80°
x°
4
4
8
9
17
4
x
18
72
Use the diagram to find the value of x.
A.
B.
C.
D.
48.
150°
Find the value of x.
A.
B.
C.
D.
47.
35°
55°
70°
110°
3
9
20
3
12
3
x
4
5
LM and LN are tangent to circle O. Find the value of x.
M
7x – 4
A.
B.
C.
D.
L
4
–8
9
–9
2x + 41
N
49.
Find the equation of the circle with center (3, –5) and radius of 5.
A.
B.
C.
D.
(x + 3)2 + (y – 5)2 = 5
(x – 3)2 + (y + 5)2 = 5
(x + 3)2 + (y – 5)2 = 25
(x – 3)2 + (y + 5)2 = 25
Page 11
Chapter 11
50.
What is the sum of the interior angles of a pentagon?
A.
B.
C.
D.
51.
180°
360°
540°
720°
An archaeologist discovered an ancient cutting tool. The tool is in the shape of a pentagon. She
hopes to learn its use by measuring the sharpness of the cutting blade, but the blade is lodged in
rock.
What is the measure, in degrees of angle x?
A.
B.
C.
D.
45
50
51
63
Note: The tool is not drawn to scale.
52.
Find the circumference of the circle.
A.
B.
C.
D.
53.
C.
D.
660 ft
11π ft
11π
ft
3
22π ft
P
A
11 ft
60°
B
Find the area of a circle if the diameter is 18 inches.
A.
B.
C.
D.
55.
6 cm
.
Find the arc length of AB
A.
B.
54.
6 cm
6π cm
12π cm
36π cm
9π inches2
18π inches2
81π inches2
162π inches2
18 in
Find the area of the shaded sector.
A.
B.
C.
D.
4π m2
9π m2
36π m2
144π m2
6m
Page 12
Chapter 12
56.
Using Eulers Theorem (F + V = E + 2) which of the following polyhedron(s) can be drawn?
I.
II.
III.
IV.
Faces
7
6
12
5
A.
B.
C.
D.
57.
I and IV only
II and III only
I, III, and IV only
III and IV only
6
8
12
14
How many faces and edges does the polyhedron shown have?
A.
B.
C.
D.
59.
Edges
16
11
23
12
If a rectangular prism has 6 faces and 12 edges, how many vertices does it have?
A.
B.
C.
D.
58.
Vertices
11
8
13
9
6 faces, 6 edges
6 faces, 12 edges
7 faces, 12 edges
9 faces, 16 edges
Which figures below are pyramids?
I.
A.
B.
C.
D.
II.
II only
I, II, IV
I and IV
all of them
III.
IV.
Page 13
60.
Which solid corresponds to the net shown at the right?
61.
What solid will be made if the net below is folded along the dotted lines?
A.
B.
C.
D.
62.
Which solid does this represent?
A.
B.
C.
D.
63.
square prism
rectangular prism
square pyramid
cone
Find the surface area of the right cylinder.
A.
B.
C.
D.
64.
cube
hexagonal prism
rectangular pyramid
rectangular prism
4 in
37π in2
40π in2
72π in2
96π in2
8 in
The surface area of the right cone is _____
A.
B.
C.
D.
33π in2
60π in2
84π in2
96π in2
8 in.
6 in.
Page 14
65.
What is the volume of the rectangular prism below?
A.
B.
C.
D.
162 in3
216 in3
288 in3
324 in3
9 in.
3 in.
12 in.
66.
Find the volume of the cone.
10 cm
A.
B.
C.
D.
13π cubic cm
30π cubic cm
60π cubic cm
90π cubic cm
3 cm
67.
Find the volume of the cylinder.
4 in
A.
B.
C.
D.
68.
13π cubic in
25π cubic in
144π cubic in
324 cubic in
9 in
Find the volume of the pyramid below with a square base.
A.
B.
C.
D.
96 cm 3
120 cm3
144 cm3
180 cm3
8
6