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Geometry Final Exam Review ~ Quadrilaterals
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 1. Judging by appearance, classify the figure in as many ways as possible.
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�
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|
|
|
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____ 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
ZW
Y
N
Short Answer
4. ABCD is a parallelogram. If then The diagram is not to scale.
5. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.
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a. rectangle, square, quadrilateral, parallelogram, rhombus
b. square, rectangle, quadrilateral
a. b.
A B
D C
O N
L M
6. Find the values of the variables in the parallelogram. The diagram is not to scale.
8. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
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: and
11. If find so that quadrilateral ABCD Page 2 of 28
x°y°
z°
10229
M N
P O
A
X
ZW
Y
N
A B
CD
is a parallelogram. The diagram is not to scale.
12. Find the values of a and b. The diagram is not to scale.
36° b°
113°a°
13. Find in the kite. The diagram is not to scale.
123
39°D B
A
C
| || || |
14. are base angles of isosceles trapezoid JKLM. If and
Page 3 of 28
Geometry Final Exam Review ~ Circles
Multiple ChoiceIdentify 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
O x°
a. 55.5 b. 69
____ 2. 12
O
x°
QP
a. 78 b. 24
____ 3. 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.
B
O
A
r
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 .
L
J
K
O
C
A B
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
BA
P
x°
a. 77 b. 38.5
____ 17. and are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.)
W
Z
X RC
Y
46
95
a. 39 b. 226
Use the diagram for # 18 - 20. is a diameter, and . The figure is not drawn to scale.
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C
A
D
BP
____ 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
C
B
a. 262 b. 246
____ 23. Find the measure of BAC. (The figure is not drawn to scale.)
A
C
O
B
a. 28.5 b. 57
____ 24. Find m BAC. (The figure is not drawn to scale.)
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A
C
O
B
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
W
Z
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a. m Zb. m(arc WZ)c. m Wd. m(arc WX)
Geometry Final Exam Review ~ Transformations
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
In the diagram, the dashed figure is the image of the solid figure.
C
D
F
E
T
S
R
S
R
Q
____ 1. Name the image of E.
a. R b. T
____ 2. Name the image of .
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. 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.
____ 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.
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____ 6. Which graph shows a triangle and its reflection image in the x-axis?
a.
2 4–2–4 x
2
4
–2
–4
y b.
2 4–2–4 x
2
4
–2
–4
y
____ 7. Describe in words the translation represented by the vector .
a. 2 units to the right and 1 units downb. 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.
A
B
C
D
E
4 8–4–8 x
4
8
–4
–8
y
____ 10. Find the vector that describes the translation B A.
a. b.
Page 9 of 28
____ 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.
4 8–4–8 x
4
8
–4
–8
y b.
4 8–4–8 x
4
8
–4
–8
y
Page 10 of 28
Geometry Final Exam Review ~ Area
Multiple ChoiceIdentify 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.
33 in.40 in.
a. 1440 in.2 b. 1188 in.2
Page 11 of 28
____ 3.
2 cm
5.4 cm
a. 7.4 cm2 b. 5.4 cm2
____ 4.
10 yd
3 yd
a. 15 yd2 b. 30 yd2
____ 5.9 cm
9 cm 11 cm
8 cm
13 cm
a. 50 cm2 b. 144.5 cm2
Page 12 of 28
____ 6.
a. 188 in.2 b. 278 in.2 c. 322 in.2 d. none of these
____ 7. 12.6 in.
29.2 in.
19 in.
14.5 in.
a. 303.66 in.2 b. 607.32 in.2
____ 8.
8 in.
7 in.
12 in.
8 in.
Not drawn to scale
a. 70 in.2 b. 77.2 in.2
____ 9. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.
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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.
8 m
8 m8 m
8 m
a. 32 m2 b. 128 m2
_
___ 15. Given the regular hexagon, find the measure of each numbered angle.
1
2
3
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
____ 22. Name the minor arc and find its measure.
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C
B
A
D ) 115°
a. arc AB; 245° b. arc AB; 115°
____ 23. Name the major arc and find its measure.
C B
A
D)50°
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
____ 26. Find the length of arc XPY. Leave your answer in terms of .
Page 15 of 28
8 m
X
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.
9105°
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
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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.
7 m
8 m
Not drawn to scale
4.
15
6
Not drawn to scale
Page 17 of 28
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.
AB
C
11 ft
Not drawn to scale
8. Find the length of the hypotenuse.
45°
3 2
9. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
Page 18 of 28
20 mi
15 mi
Dunlap Butte
Ferris5. Wayne used the diagram to compute the distance from
Ferris to Dunlap to Butte. How much shorter is the dis-tance directly from Ferris to Butte than the distance Wayne found?
45°
16
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.
7
x
y
45°
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
12.30°
y
x
17
Not drawn to scale
13. Find the value of x and y, rounded to the nearest tenth.
Page 19 of 28
x 34
30°45°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 .
Find the value of x. Round your answer to the nearest tenth.
16.x
7
Not drawn to scale
Find the value of x to the nearest degree.Page 20 of 28
R Q
P
21
20
29
Not drawn to scale
17.11
19
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.
A249 ft
100 ft
20. Write the ratios for sin A and cos A.
Page 21 of 28
C B
A
4
3
5
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 22 of 28
Geometry Final Exam Review ~ Similarity (Ratio & Proportion)
Multiple ChoiceIdentify 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?
x
8 m4 m
12 m
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.
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6.
7. . Complete the statements.
D C
E B
A
J
H
G
F
a.
b.ABGH
DJ
8. Figure . Name a pair of corresponding sides?
10. What is the measure of ?
Q S
R
T V
UU)
)
)) ))63°
47°
Page 24 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 25 of 28
Geometry Final Exam Review ~ QuadrilateralsAnswer Section
MULTIPLE CHOICE
1. ANS: A2. ANS: A3. 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 ~ CirclesAnswer Section
MULTIPLE CHOICE
1. ANS: B2. ANS: A3. ANS: B
5. ANS: A
10. ANS: A17. ANS: B18. ANS: B19. ANS: A20. ANS: A22. ANS: A
Page 26 of 28
23. ANS: A24. ANS: A
SHORT ANSWER
33. ANS:a. 30b. 150c. 88d. 34
Geometry Final Exam Review ~ TransformationsAnswer Section
MULTIPLE CHOICE
1. A2. A3. A4. B5. A6. A7. A8. A9. A
10. A11. A12. A13. A14. B
Geometry Final Exam Review ~ AreaAnswer Section
MULTIPLE CHOICE
1. ANS: A2. ANS: B3. ANS: B4. ANS: A5. ANS: B6. ANS: B7. ANS: A8. ANS: A9. ANS: B
13. ANS: A14. ANS: B
Page 27 of 28
15. ANS: B16. ANS: B22. ANS: B23. ANS: A24. ANS: A25. ANS: A26. ANS: B27. ANS: A28. ANS: A29. ANS: B
Geometry Final Exam Review ~ Right TrianglesAnswer Section
SHORT ANSWER
1. 102. 73. 113 m
4. 3 21 cm5. 10 mi6. no; 7. 15.6 ft8. 69. 8 2
10. x = 9.9, y = 711.12. x = , y = 3413. x = 24.0, y = 46.414. 6 + 2
15.
16. 417. 6018. 308 ft19. 22
20.
21. 12.522. 8.1
Page 28 of 28
Geometry Final Exam Review ~ Similarity (Ratio & Proportion)Answer Section
MULTIPLE CHOICE
1. B
SHORT ANSWER
2. 18 : 13. 1 : 7254. 95. 25
6.
7. ; DC8.
10. 7011. 80 ft12. 20 ft
Page 29 of 28
