Name: ______________________________
Geometry Final Exam Review ~ Quadrilaterals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Judging by appearance, classify the figure in as many ways as possible.
•
____
•
•
|
|
•
|
|
a. rectangle, square, quadrilateral, parallelogram,
rhombus
b. square, rectangle, quadrilateral
____
2. Which statement is true?
a. All rectangles are quadrilaterals.
b. All quadrilaterals are parallelograms.
____
3. WXYZ is a parallelogram. Name an angle congruent to
X
Y
a.
b.
N
W
Z
Short Answer
A
B
4. ABCD is a parallelogram. If
then
The diagram is not to scale.
D
5. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5
find the value of x and then find NM and OL.
O
N
L
Page 1 of 28
C
M
6. Find the values of the variables in the parallelogram.
The diagram is not to scale.
29
102
y°
z°
8. Find AM in the parallelogram if PN =9 and AO = 4.
The diagram is not to scale.
x°
M
N
A
P
O
9. Based on the information in the diagram, can you
prove that the figure is a parallelogram? Explain.
10. Based on the information given, can you determine
that the quadrilateral must be a parallelogram? Explain.
Given:
X
and
Y
N
W
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Z
A
11. If
find
so that quadrilateral ABCD
is a parallelogram. The diagram is not to scale.
D
C
12. Find the values of a and b. The diagram is not to scale.
a°
113°
36°
b°
13. Find
in the kite. The diagram is not to scale.
|
3
2
B
||
||
D
1
|
A
39°
C
14.
are base angles of isosceles trapezoid JKLM. If
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B
and
Geometry Final Exam Review ~ Circles
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures
are not drawn to scale.)
____
1.
111
x°
O
a. 55.5
____
2.
b. 69
12
Q
P
x°
O
a. 78
____
3.
b. 24
is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest
tenth if necessary. The diagram is not to scale.
A
B
r
O
a. 9.9
b. 7
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____
5.
and
are all tangent to O (not drawn to scale). JA = 9, AL = 10, and
CK = 14. Find the perimeter of
.
J
A
B
O
L
K
C
a. 66
b. 46
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.
____ 10.
D
C

P
x°
A
B
a. 77
____ 17.
b. 38.5
and
are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.)
Y
Z
95
X
46
C
R
W
a. 39
b. 226
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Use the diagram for # 18 - 20.
is a diameter, and
. The figure is not drawn to scale.
C
P
A
B
D
____ 18. Find
for
= 66.
a. 114
b. 57
____ 19. Which statement is NOT true?
a. arc AC
arc BD
b.
____ 20. Find m(arc BD) for m(arc AC) = 43°.
a. 137°
b. 133°
____ 22. Given that DAB and DCB are right angles and m BDC = 41, what is the measure of arc CAD? (The figure
is not drawn to scale.)
A
D
B
C
a. 262
b. 246
____ 23. Find the measure of BAC. (The figure is not drawn to scale.)
A
O

C
B
a. 28.5
b. 57
Page 6 of 28
____ 24. Find m BAC. (The figure is not drawn to scale.)
A

O
B
C
a. 57
b. 132
Short Answer
33. Given: m X = 150,
, m Y = 92. Find each measurement. (The figure is not drawn to scale.)
Y
X
Z
a.
b.
c.
d.
m Z
m(arc WZ)
m W
m(arc WX)
W
Page 7 of 28
Geometry Final Exam Review ~ Transformations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
In the diagram, the dashed figure is the image of the solid figure.
D
R
E
S
C
____
T
.
b.
b.
4. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of the image reflected in
the y-axis.
a.
____
b.
3. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of the image reflected in the
x-axis.
a.
____
R
2. Name the image of
a.
____
Q
T
1. Name the image of E.
a.
____
F
b.
5. The vertices of a triangle are P(–7, –4), Q(–7, –8), and R(3, –3). Name the vertices of the image reflected in
the line y = x.
a.
b.
Page 8 of 28
____
6. Which graph shows a triangle and its reflection image in the x-axis?
a.
–4
____
b.
y
y
4
4
2
2
–2
2
4
–4
x
–2
2
–2
–2
–4
–4
7. Describe in words the translation represented by the vector
4
.
a. 2 units to the right and 1 units down
b. 1 units to the right and 2 units down
____
8. Use an ordered pair to describe the translation that is 7 units to the left and 1 units down.
a.
____
b.
9. Use an ordered pair to describe the translation that is 8 units to the right and 2 units up.
a.
b.
Use the diagram for # 10 & 11.
y
E8
4
C
–8
A
–4
4
–4
8
x
D
B
–8
____ 10. Find the vector that describes the translation B
a.
A.
b.
Page 9 of 28
x
____ 11. Find the image of C under the translation described by the vector
a. B
.
b. E
____ 12. Write a rule to describe the transformation that is a reflection in the x-axis.
a. (x, y)  (x, –y)
b. (x, y)  (–x, y)
____ 13. Write a rule to describe the transformation that is a reflection in the y-axis.
a. (x, y)  (–x, y)
b. (x, y)  (x, –y)
____ 14. Which translation from the solid-lined figure to the dashed-lined figure is given by the vector
a.
b.
y
–8
y
8
8
4
4
–4
4
8
x
–8
–4
4
–4
–4
–8
–8
Page 10 of 28
8
x
?
Geometry Final Exam Review ~ Area
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Find the area. The figure is not drawn to scale.
____
1.
7.6 cm
3.7 cm
a.
____
b.
2.
36 in.
40 in.
33 in.
a. 1440 in.2
____
b. 1188 in.2
3.
2 cm
5.4 cm
2
b. 5.4 cm2
a. 7.4 cm
____
4.
3 yd
10 yd
a. 15 yd2
b. 30 yd2
Page 11 of 28
____
5.
9 cm
8 cm
13 cm
9 cm
11 cm
a. 50 cm2
____
b. 144.5 cm2
6.
a. 188 in.2
____
b. 278 in.2
c. 322 in.2
7.
19 in.
12.6 in.
14.5 in.
29.2 in.
a. 303.66 in.2
____
b. 607.32 in.2
8.
8 in.
7 in.
8 in.
12 in.
Not drawn to scale
a. 70 in.2
b. 77.2 in.2
Page 12 of 28
d. none of these
____
9. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.
a. 385 cm
b. 12 cm
____ 13. A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?
a. 36.8 ft2
b. 8.6 ft2
____ 14. Find the area of the rhombus.
8m
8m
8m
8m
a. 32 m2
b. 128 m2
_
___
15. Given the regular hexagon, find the measure of each numbered angle.
3
1
2
a.
b.
____ 16. Find the area of a regular hexagon with an apothem 16.5 feet long and a side 19 feet long. Round your answer
to the nearest tenth.
a. 156.3 ft2
b. 937.9 ft2
Page 13 of 28
____ 22. Name the minor arc and find its measure.
A
D
C
) 115°
B
a. arc AB; 245°
b. arc AB; 115°
____ 23. Name the major arc and find its measure.
A
D
C
)50°
B
a. arc ADB; 310
b. arc AB; 50
Find the circumference. Leave your answer in terms of .
____ 24.
18 in.
a.
in.
b.
in.
____ 25. The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140°.
a. 60 cm; 30 cm; 23.3 cm
b. 120 cm; 30 cm; 160 cm
Page 14 of 28
____ 26. Find the length of arc XPY. Leave your answer in terms of .
X
8m
Y
P
a. 720 m
b. 12 m
Find the area of the circle. Leave your answer in terms of .
____ 27.
3.6 m
a. 12.96 m2
b. 46.66 m2
_
___
28. Find the area of the figure to the nearest tenth.
105°
9
a. 74.2 in.2
b. 148.4 in.2
____ 29. Find the area of a sector with a central angle of 180° and a diameter of 5.6 cm. Round to the nearest tenth.
a. 49.2 cm2
b. 12.3 cm2
Page 15 of 28
Geometry Final Exam Review ~ Right Triangles
Short Answer
Find the length of the missing side. Figures are not drawn to scale.
1.
6
8
2.
25
24
Find the length of the missing side. Leave
your answer in simplest radical form.
3.
8m
7m
Not drawn to scale
4.
15
6
Not drawn to scale
Page 16 of 28
5. Wayne used the diagram to compute the distance from
Ferris to Dunlap to Butte. How much shorter is the distance directly from Ferris to Butte than the distance
Wayne found?
Ferris
15 mi
Dunlap
20 mi
Butte
6. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.
7. In triangle ABC,
is a right angle and
45. Find BC. Round your answer to the nearest tenth.
C
11 ft
B
A
Not drawn to scale
8. Find the length of the hypotenuse.
45°
3 2
Page 17 of 28
9. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
16
45°
Not drawn to scale
10. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals
rounded to the nearest tenth.
y
7
45°
x
Not drawn to scale
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
11.
6
x
60°
12
Not drawn to scale
12.
y
17
30°
x
Not drawn to scale
Page 18 of 28
13. Find the value of x and y, rounded to the nearest tenth.
x
34
45°
30°
y
14. The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the perimeter.
15. Write the tangent ratios for
and
P
.
29
21
R
20
Not drawn to scale
Find the value of x. Round your answer to the nearest tenth.
16.
7

x
Not drawn to scale
Page 19 of 28
Q
Find the value of x to the nearest degree.
17.
19
11
x
Not drawn to scale
18. 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.
Building

100 ft
19. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts
a 249-foot-long shadow. Find the measure of
to the nearest degree.
100 ft
A
249 ft
Page 20 of 28
20. Write the ratios for sin A and cos A.
A
5
4
C
B
3
Not drawn to scale
Find the value of x. Round to the nearest tenth.
21.
x

11
Not drawn to scale
22.
10

x
Not drawn to scale
Page 21 of 28
Geometry Final Exam Review ~ Similarity (Ratio & Proportion)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. The two rectangles are similar. Which is a correct proportion for corresponding sides?
4m
8m
12 m
x
a.
b.
Short Answer
2. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length
of the car to the length of the model?
3. 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?
Solve the proportion.
4.
5.
6.
Page 22 of 28
7.
. Complete the statements.
A
G
E
B
F
H
D
J
C
a.
GH
b.

AB
DJ
8. Figure
. Name a pair of corresponding sides?
10.
What is the measure of
?
R
)
U
)
47°
63°
))
Q
))
S
T
V
Page 23 of 28
11. Use the information in the diagram to determine the height of the tree to the nearest foot.
12. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet
from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes
were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of
the flagpole to the nearest tenth of a foot.
Page 24 of 28
Geometry Final Exam Review ~ Quadrilaterals
Answer Section
MULTIPLE CHOICE
1. ANS: A
2. ANS: A
3. ANS: B
SHORT ANSWER
4. ANS:
114
5. ANS:
x = 5, NM = 20, OL = 20
6. ANS:
8. ANS:
4
9. ANS:
Yes; opposite angles are congruent.
10. ANS:
Yes; opposite sides are congruent.
11. ANS:
139
12. ANS:
13. ANS:
39, 51
14. ANS:
151
Geometry Final Exam Review ~ Circles
Answer Section
MULTIPLE CHOICE
1.
2.
3.
5.
ANS:
ANS:
ANS:
ANS:
B
A
B
A
10.
17.
18.
19.
20.
22.
23.
24.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
B
A
A
A
A
A
Page 25 of 28
SHORT ANSWER
33. ANS:
30
a.
150
b.
88
c.
34
d.
Geometry Final Exam Review ~ Transformations
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
A
A
A
B
A
A
A
A
A
A
A
A
A
B
Geometry Final Exam Review ~ Area
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
13.
14.
15.
16.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
B
A
B
B
A
A
B
A
B
B
B
Page 26 of 28
22.
23.
24.
25.
26.
27.
28.
29.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
A
A
A
B
A
A
B
Geometry Final Exam Review ~ Right Triangles
Answer Section
SHORT ANSWER
1. 10
2. 7
3.
113 m
4. 3 21 cm
5. 10 mi
6. no;
7. 15.6 ft
8. 6
9. 8 2
10. x = 9.9, y = 7
11.
12. x =
, y = 34
13. x = 24.0, y = 46.4
14. 6 + 2
15.
16.
17.
18.
19.
4
60
308 ft
22
20.
21. 12.5
22. 8.1
Page 27 of 28
Geometry Final Exam Review ~ Similarity (Ratio & Proportion)
Answer Section
MULTIPLE CHOICE
1. B
SHORT ANSWER
2.
3.
4.
5.
18 : 1
1 : 725
9
25
6.
7.
; DC
8.
10. 70
11. 80 ft
12. 20 ft
Page 28 of 28