Download Geometry Review of material to date for the Final Exam: Ch. 1-12

Geometry Review of material to date for the Final Exam: Ch. 1-12
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Name the ray in the figure.
4. If T is the midpoint of
A
B
SU?
S
a.
what are ST, TU, and
T
9x
U
6 x + 30
b.
a.
b.
c.
d.
c.
d.
2. What is the name of the ray that is opposite
ST = 10, TU = 90, and SU = 180
ST = 110, TU = 110, and SU = 220
ST = 18, TU = 18, and SU = 36
ST = 90, TU = 90, and SU = 180
?
5.
bisects
and
Solve for x and find
The diagram is not to scale.
D
C
B
A
a.
b.
c.
d.
3. What is the intersection of plane TUYX and plane
VUYZ?
a.
b.
c.
d.
x = 13,
x = 13,
x = 14,
x = 14,
6. Noam walks home from school by walking 8
blocks north and then 6 blocks east. How much
shorter would his walk be if there were a direct path
from the school to his house? Assume that the
blocks are square.
a. 14 blocks
b. 10 blocks
c. 4 blocks
d. The distance would be the same.
a.
b.
c.
d.
7. Find the circumference of the circle in terms of .
39 in.
a.
b.
c.
d.
156 in.
39 in.
1521 in.
78 in.
8. Find the area of a rectangle with base of 2 yd and a
height of 5 ft.
a. 10 yd
b. 30 ft
c. 10 ft
d. 30 yd
12. Is the statement a good definition? If not, find a
counterexample.
A square is a figure with two pairs of parallel sides
and four right angles.
a. The statement is a good definition.
b. No; a rhombus is a counterexample.
c. No; a rectangle is a counterexample.
d. No; a parallelogram is a counterexample.
13.
a.
b.
c.
d.
bisects
. Find
50
125
75
175
14.
= 7x.
Find
1
4
9. What conjecture can you make about the fourteenth
term in the pattern A, B, A, C, A, B, A, C?
a. The fourteenth term is B.
b. The fourteenth term is C.
c. The fourteenth term is A.
d. There is not enough information.
10. Write this statement as a conditional in if-then
form:
All triangles have three sides.
a. If a triangle has three sides, then all triangles
have three sides.
b. If a figure has three sides, then it is not a
triangle.
c. If a figure is a triangle, then all triangles have
three sides.
d. If a figure is a triangle, then it has three sides.
11. Is the following definition of perpendicular
reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are
perpendicular.
a. The statement is not reversible.
b. Yes; if two lines intersect at right angles, then
they are perpendicular.
c. Yes; if two lines are perpendicular, then they
intersect at right angles.
d. Yes; two lines intersect at right angles if (and
only if) they are perpendicular.
=
2
3
Drawing not to scale
a.
b.
c.
d.
37
143
27
153
15. What is the relationship between
1
2
m
3
4
5
6
n
7
a.
b.
c.
d.
8
corresponding angles
same-side interior angles
alternate interior angles
alternate exterior angles
and
?
y
16. Find the value of x for which p is parallel to q, if
.The diagram is not to
scale.
10
8
6
(–8, 5)
3 4
5
4
2
1 2
6
–10 –8 –6 –4 –2
–2
2
4
6
8 10
x
–4
p
–6
q
–8
a.
b.
c.
d.
(1, –8)
–10
108
116
28
112
a.
17. Find the value of x for which l is parallel to m. The
diagram is not to scale.
80°
( 3 x - 43 )º
l
9
13
b.
13

9
c. 13
9
d.
9

13
m
20. What is the slope of the line shown?
a.
b.
c.
d.
y
100
80
123
41
8
6
4
2
18. Find the values of x, y, and z. The diagram is not to
scale.
–8 –6 –4 –2
–2
35°
(–8, –5)
11°
59°
x°
z°
2
4
(5, 0)
6 8
x
–4
–6
–8
y°
a.
a.
b.
c.
d.
19. What is the slope of the line shown?
13
5
b.
13

5
c. 5
13
d.
5

13
21. What is the equation in point-slope form for the line
parallel to y = 3x + 2 that contains P(–7, –6)?
y – 6 = 3(x + 7)
x + 6 = –3(y + 7)
y + 6 = –3(x + 7)
y + 6 = 3(x + 7)
a.
b.
c.
d.
a.
b.
c.
d. none of these
22. Given
and
, find
a.
b.
c.
d.
24. State whether
and
Justify your answer.
and
22
11
10
25
7
23. Name the angle included by the sides
N
7
and
M
a.
b.
c.
d.
P
25. What is the missing reason in the two-column proof?
Given:
Prove:
bisects
and
bisects
N
<
are congruent.
M
O
>
P
Statements
Reasons
1.
2.
3.
bisects
1. Given
2. Definition of angle bisector
3. Reflexive property
4.
5.
6.
bisects
4. Given
5. Definition of angle bisector
6. ?
a. ASA Postulate
c. AAS Theorem
yes, by either SSS or SAS
yes, by SSS only
yes, by SAS only
No; there is not enough information to
conclude that the triangles are congruent.
b. SSS Postulate
26. What is the value of x?
d. SAS Postulate
29. Use the information in the diagram to determine the
height of the tree. The diagram is not to scale.
38°
21
150 ft
21
xº
a.
b.
c.
d.
Drawing not to scale
a.
b.
c.
d.
71°
142°
152°
76°
75 ft
150 ft
35.5 ft
37.5 ft
30. Name a median for
A
27. Find the value of x. The diagram is not to scale.
|
S
E
)
|
|
|
D
)
(3 x – 50)°
R
(7 x )°
T
U
a.
b.
c.
d. none of these
28. Which overlapping triangles are congruent by
ASA?
a.
b.
c.
d.
C
F B
a.
b.
c.
d.
31. For a triangle, list the respective names of the
points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes
a. incenter
circumcenter
centroid
orthocenter
b. circumcenter
incenter
centroid
orthocenter
c. circumcenter
incenter
orthocenter
centroid
d. incenter
circumcenter
orthocenter
centroid
32. Name the second largest of the four angles named
in the figure (not drawn to scale) if the side
included by
and
is 11 cm, the side included
by
and
is 16 cm, and the side included by
and
is 14 cm.
35. This jewelry box has the shape of a regular
pentagon. It is packaged in a rectangular box as
shown here. The box uses two pairs of congruent
right triangles made of foam to fill its four corners.
Find the measure of the foam angle marked.
x
x
1
2
3
4
a.
b.
c.
d.
33. Find the sum of the measures of the angles of the
figure.
a.
b.
c.
d.
18°
54°
36°
72°
36. Use less than, equal to, or greater than to complete
this statement: The sum of the measures of the
exterior angles of a regular 5-gon, one at each
vertex, is ____ the sum of the measures of the
exterior angles of a regular 9-gon, one at each
vertex.
a. greater than
b. cannot tell
c. equal to
d. less than
37. ABCD is a parallelogram. If
then
The diagram is not to scale.
A
a.
b.
c.
d.
900
1080
1620
1260
34. What is the measure of one angle in a regular 25gon?
a.
b.
c.
d.
B
194.4
4140
165.6
82.8
D
a.
b.
c.
d.
C
66
124
114
132
38. For the parallelogram, if
find
scale.
and
The diagram is not to
3
A
4
2
B
4x – 2
1
y + 14
9
17
173
163
4y – 7
x + 28
39. ABCD is a parallelogram. If
then
The diagram is not to scale.
A
B
D
a.
b.
c.
d.
C
x = 10, y = 38
x = 10, y = 21
x = 10, y = 7
x = 7, y = 10
42. In the rhombus,
C
1
|
D
What are
The diagram is not to scale.
|
a.
b.
c.
d.
125
65
75
115
3
|
|
a.
b.
c.
d.
2
40. If
find
so that
quadrilateral ABCD is a parallelogram. The
diagram is not to scale.
A
D
a.
b.
c.
d.
B
C
a.
b.
c.
d.
43. The isosceles trapezoid is part of an isosceles
triangle with a 46° vertex angle. What is the
measure of an acute base angle of the trapezoid? Of
an obtuse base angle? The diagram is not to scale.
39
282
141
78
41. Find values of x and y for which ABCD must be a
parallelogram. The diagram is not to
scale.
a. 67°; 134°
b. 67°; 113°
c. 46°; 134°
d. 46°; 113°
d. 95.5
45. The Sears Tower in Chicago is 1450 feet high. A
model of the tower is 24 inches tall. What is the
ratio of the height of the model to the height of the
actual Sears Tower?
a. 1 : 725
b. 725 : 1
c. 12 : 725
d. 725 : 12
44.
What is LM?
A
B
L
M
D
46. The ratio of length to width in a rectangle is 3 to 1.
If the perimeter of the rectangle is 128 feet, what is
the length of the rectangle?
a. 32 feet
b. 48 feet
c. 64 feet
d. 96 feet
C
a. 171
b. 85.5
c. 79
What is the solution of each proportion?
47.
a.
b.
c.
d.
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
S
V
10
12
T
15
32º
W
R
32º
U
18
Not drawn to scale.
48.
a.
b.
;
;
c.
;
d. The triangles are not similar.
A
21.6
B
N
1.8
K
9
9
4.68
4.68
D
M
C
21.6
1.8
L
Not drawn to scale.
49.
a.
b.
50.
; 9 : 1.8
; 21.6 : 1.8
c.
; 9 : 4.68
d. The polygons are not similar.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
a. 118
b. 29.5
c. 21.7
d. 177
52. Are the triangles similar? How do you know?
30.4°
a. x = 8
b.
x=
84.6°
a.
b.
c.
d.
c. x = 9
d. x = 10
K
yes, by SAS
yes, by SSS
yes, by AA
no
B
J
A
L
C
6
3
59
x
D
51.
M
Which theorem or postulate proves the two triangles are similar?
84.6°
66°
c.
53.
14
d.
28
>
7
56. What is value of x, given that
?
>
O
Not drawn to scale.
a.
b.
c.
d.
SSS Theorem
AA Postulate
AS Postulate
SAS Theorem
x
Q
18
54. Use the information in the diagram to determine the
height of the tree to the nearest foot.
a.
b.
c.
d.
P
9
N
20
M
a.
b.
c.
d.
x = 10
x = 20
x = 13
x = 25.5
57. Four explorers are trying to find the distance across
an oddly shaped lake. They position themselves as
shown in the diagram. Alhombra uses her compass
to instruct Chou and Duong to move along the line
they form with Bizet until she sees that from her
perspective the angle between Bizet and Chou is
equal to the angle formed between Chou and
Duong. They measure the distance between Bizet
and Chou to be 35 m, between Chou and Duong to
be 46 m, and between Alhombra and Duong to be
100 m. How long is the lake from east to west?
Round your answer to the nearest tenth of a meter.
80 ft
264 ft
60 ft
72 ft
55. What is the value of x, given that
?
A
x
B
11
E 5 D
7
C
a.
b.
a.
b.
c.
d.
76.1 m
77.4 m
131.4 m
132.4 m
58. A triangle has side lengths of 28 in, 4 in, and 31 in.
b. right
Classify it as acute, obtuse, or right.
c. acute
a. obtuse
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
b. 42 ft; 35 min
59.
c. 14 ft; 1 min
d. 28 ft; 0.4 min
x
y
62. Find the missing value to the nearest hundredth.
30°
tan
20
Not drawn to scale
a.
b.
c.
d.
a. x =
,y=
b. x = 10, y =
c. x =
, y = 10
d. x = 30, y =
= 86
44.67
89.67
89.33
51.67
63. Write the tangent ratios for
and
.
Z
60. A sign is in the shape of a rhombus with a 60°
angle and sides of 9 cm long. Find its area to the
nearest tenth.
a. 70.1 cm2
b. 3.9 cm2
c. 7.8 cm2
d. 35.1 cm2
61. A conveyor belt carries supplies from the first floor
to the second floor, which is 24 feet higher. The
belt makes a 60° angle with the ground.
34
3
X
5
Y
Not drawn to scale
a.
b.
How far do the supplies travel from one end of the
conveyor belt to the other? Round your answer to
the nearest foot.
If the belt moves at 75 ft/min, how long, to the
nearest tenth of a minute, does it take the supplies
to move to the second floor?
a. 34 ft; 21 min
Find the value of x. Round to the nearest tenth.
c.
d.
d. 8.1
64.
10

x
Not drawn to scale
a. 12.9
b. 8.5
c. 12.4
65. The students in Mr. Collin’s class used a surveyor’s
measuring device to find the angle from their
location to the top of a building. They also
measured their distance from the bottom of the
building. The diagram shows the angle measure and
the distance. To the nearest foot, find the height of
the building.
a.
b.
c.
d.
2400 ft
72 ft
308 ft
33 ft
Building

100 ft
Find the value of x. Round to the nearest degree.
66.
21
x
15
Not drawn to scale
a. 41
b. 36
c. 46
d. 44
c. 70
d. 85
Find the value of x to the nearest degree.
67.
19
11
x
Not drawn to scale
a. 30
b. 60
Find the value of x. Round the length to the nearest tenth.
68.
b. 10.4 yd
c. 9 yd
d. 31.2 yd

x
18 yd
Not drawn to scale
a. 15.6 yd
69. To find the height of a pole, a surveyor moves 140
feet away from the base of the pole and then, with a
transit 4 feet tall, measures the angle of elevation to
the top of the pole to be 44 . To the nearest foot,
what is the height of the pole?
a. 145 ft
b. 149 ft
c. 135 ft
d. 139 ft
Use compass directions to describe the direction of the vector.
(Not drawn to scale.)
70.
N

W
E
S
a. 47 north of west
b. 47 south of west
c. 47 north of east
d. 47 south of east
Use the diagram.
y
E8
4
C
–8
A
–4
4
–4
8
x
D
B
–8
71. Find the translation rule that describes the translation B
a.
c.
b.
d.
A.
72. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of the image reflected across
the y-axis.
a.
c.
b.
d.
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles.
F
R
G
Q
H
P
I
O
N
J
M
L
K
73. Find the image of
after a rotation of 240° about
point O.
a.
b.
c.
d.
Find the area. The figure is not drawn to scale.
75.
74. Find the angle of rotation about O that maps P to G.
a. 240°
b. 120°
c. 210°
d. 270°
c. 13 yd2
d. 15 yd2
36 in.
77.
40 in.
33 in.
9 cm
8 cm
a.
b.
c.
d.
1188 in.2
69 in.2
138 in.2
1440 in.2
13 cm
76.
9 cm
3 yd
10 yd
a.
b.
c.
d.
11 cm
144.5 cm2
127 cm2
172 cm2
50 cm2
a. 30 yd2
b. 6.5 yd2
Find the area of a parallelogram with the given vertices.
78. P(1, 3), Q(3, 3), R(7, 8), S(9, 8)
79. Find the area of the regular polygon. Round your
a. 10 units2
answer to the nearest tenth.
b. 5 units2
c. 20 units2
d. none of these
81. The triangles are similar. The area of the larger
triangle is 1589 ft . Find the area of the smaller
triangle to the nearest whole number.
40 ft
13.07 in.
35 ft
10 in.
a.
b.
c.
d.
Not drawn to scale
2
176.6 in.
966.1 in.2
80.0 in.2
483.0 in.2
80. The area of a regular octagon is 35 cm . What is
the area of a regular octagon with sides three times
as long?
a. 315 cm
b. 225 cm
c. 175 cm
d. 105 cm
a.
b.
c.
d.
1217 ft
1225 ft
1600 ft
2075 ft
82. Find the similarity ratio and the ratio of perimeters
for two regular octagons with areas of
and
a. 3 : 5; 3: 5
b. 9 : 25; 3 : 5
c. 3 : 5; 9 : 25
d. 9 : 25; 9 : 25
Find the area of the regular polygon. Give the answer to the nearest tenth.
83. hexagon with a side of 8 yd
86. Identify a semicircle that contains C.
a. 332.6 yd
b. 12 yd
C
c. 41.6 yd
d. 166.3 yd
A
84. pentagon with a radius of 8 m
a. 304.3 m
b. 152.2 m
c. 30.4 m
d. 154.2 m
85. Divers looking for a sunken ship have defined the
search area as a triangle with adjacent sides of
length 2.75 miles and 1.32 miles. The angle
between the sides of the triangle is 35 . To the
nearest hundredth, find the search area.
a. 2.08 mi
b. 2.97 mi
c. 1.04 mi
d. 1.49 mi
B
0
a.
b.
c.
d.
87. Name the major arc and find its measure.
A
A
E
D
C
)50°
103°
B
27°
D
50°
B
35°
O
C
a.
b.
c.
d.
; 50
; 50
; 310
a.
b.
c.
d.
130
230
140
120
; 310
88. Find the measure of
.
The figure is not drawn to scale.
Find the area of the circle. Leave your answer in terms of .
a.
89.
b.
c.
d.
74.2 in.2
8.2 in.2
148.4 in.2
23.6 in.2
4.1 m
92. Find the area of the shaded region. Leave your
answer in terms of and in simplest radical form.
a.
b.
c.
d.
4.2025 m2
8.405 m2
16.81 m2
11.2 m2
90. A team in science class placed a chalk mark on the
side of a wheel and rolled the wheel in a straight
line until the chalk mark returned to the same
position. The team then measured the distance the
wheel had rolled and found it to be 35 cm. To the
nearest tenth, what is the area of the wheel?
a. 195.1 cm2
b. 97.5 cm2
c. 27.5 cm2
d. 390.1 cm2
91. Find the area of the figure to the nearest tenth.
a.
b.
c.
d. none of these
93. Find the probability that a point chosen at random
from
is on the segment
.
A B C D E F G H I
0
a.
105°
9
2
4
6
8
J K
10
b.
96. The radius of the base of a cylinder is 39 in. and its
height is 33 in.. Find the surface area of the
cylinder in terms of .
a. 5583 in.
b. 5577 in.
c. 5688 in.
d. 5616 in.
c.
d.
94. Find the probability that a point chosen at random
will lie in the shaded area.
97. Find the surface area of the cone in terms of
.
17 cm
14
3 cm
Not drawn to scale
a.
b.
c.
d.
a.
b.
c.
d.
0.32
0.62
0.94
0.02
95. A circular dartboard has a radius of 2 meters and a
red circle in the center. Assume you hit the target at
a random point. For what radius of the red center
region does P(hitting red) = 0.6?
a. 77 m
b. 1.2 m
c. 1.55 cm
d. 1.32 m
Find the volume of the cylinder in terms of
111 cm
57 cm
60 cm
55.5 cm
98. The lateral area of a cone is 558 cm . The radius
is 31 cm. Find the slant height to the nearest tenth.
a. 17.1 cm
b. 16.4 cm
c. 18 cm
d. 11.6 cm
.
c. 54 in.
d. 324 in.
99.
h = 6 and r = 3
a. 27 in.
b. 108 in.
100.
5 in.
14 in.
6 mm
11 mm
9 mm
Not drawn to scale
a.
b.
c.
d.
Not drawn to scale
140 in.
175 in.
350 in.
70 in.
101. Find the volume of the composite space figure to
the nearest whole number.
a.
b.
c.
d.
416 mm
705 mm
1294 mm
944 mm
102. Two square pyramids have the same volume. For
the first pyramid, the side length of the base is 20
in. and the height is 21 in. The second pyramid has
a height of 84 in. What is the side length of the base
of the second pyramid?
a. 10 in.
b. 21 in.
c. 28 in.
d. 42 in.
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
103.
17 yd
8 yd
Not drawn to scale
a. 2421.1 yd
In the figure,
b. 1709 yd
and
c. 142.4 yd
are tangent to circle O and
d. 1139.4 yd
bisects
. The figure is not drawn to scale.
B
D
O
C
A
P
104. For
a. 40
105.
= 50, find
.
b. 50
c. 65
d. 140
is tangent to circle A at B and to circle D at C (not drawn to scale).
AB = 10, BC = 21, and DC = 8. Find AD to the nearest tenth.
B
C
A
D
a. 22.5
b. 21.1
c. 23.3
106. Pentagon RSTUV is circumscribed about a circle.
Solve for x for RS = 10, ST = 13,
TU = 11, UV = 12, and VR = 12. The figure is not
drawn to scale.
R
107.
x
V
S
U
T
d. 27.7
a.
b.
c.
d.
4
8
11
6
The radius of circle O is 18, and OC = 13. Find AB.
Round to the nearest tenth, if necessary. (The figure
is not drawn to scale.)
a.
b.
c.
d.
C
A
B
57
28.5
33
114
109. In the circle,
. Find m BCP.
(The figure is not drawn to scale.)
O
a.
b.
c.
d.
A
12.4
3.8
24.9
44.4
D
B
108. Find the measure of
drawn to scale.)
Q
BAC. (The figure is not
C
P
A
a.
b.
c.
d.
49
98
196
82
O
57º
C
B
110.
and
. Find m A. (The figure is not drawn to scale.)
D
B
A
C
E
a. 32.5
b. 65
c. 95.5
111. A footbridge is in the shape of an arc of a circle.
The bridge is 4.5 ft tall and 25 ft wide. What is the
radius of the circle that contains the bridge? Round
to the nearest tenth.
a. 39.2 ft
b. 71.7 ft
c. 19.6 ft
d. 34.7 ft
112. Find the diameter of the circle for BC = 13 and DC
= 24. Round to the nearest tenth.
(The diagram is not drawn to scale.)
Describe the locus in space.
113. points 5 cm from a point C
a. a sphere of radius 5 cm, centered at C
b. a circle of radius 5 cm, centered at C
c. an endless cylinder with radius 5 cm
d. a hemisphere of radius 5 cm, centered at C
114. points 3 in. from plane K
a. a circle of radius 3 cm, centered at K
b. two planes parallel to plane K, each 3 in. from
K
c. two lines parallel to plane K, each 3 in. from K
d. a sphere of radius 3 cm, centered at K
d. 96.5
D
C
B
O
A
a.
b.
c.
d.
31.3
44.3
11.2
57.3