FINAL EXAM Review Chapters 7,8,9. · 2016-05-16 · FINAL EXAM Review Chapters 7,8,9. ____ 1. Find the sum of the measures of the interior angles of a convex hexagon. ... Estimate

FINAL EXAM Review Chapters 7,8,9.

____ 1. Find the sum of the measures of the interior angles of a convex hexagon.

a. 900° c. 1080°

b. 720° d. 1440°

____ 5. Find the value of x.

a. about 27.6 c. about 57.6

b. about 42.6 d. about 12.6

____ 7. Find the value of x.

a. 3 c. 57

b. 27 d. 81

____ 9. Find the values of x and y in the parallelogram.

a. , c. ,

b. , d. ,

6x°

102°

132°

140 °

132°6x°

124 °

119°

56 °

2x°

85°

57°

4x°

D A

BC

x – 224

11

y

____ 12. Find when quadrilateral ABCD is a parallelogram.

a. 57° c. 123°

b. 147° d. 33°

____ 13. Find the coordinates of the intersection of the diagonals of with vertices , ,

, and .

a. c.

b. d.

____ 14. Three vertices of are . Find the coordinates of .

a. c.

b. d.

Find the measures of the numbered angles in rhombus QRST.

____ 17.

a. , , ,

b. , , ,

c. , , ,

d. , , ,

____ 20. Find the lengths of the diagonals of rectangle QRST when and .

a. 35 c. 70

b. 99.7 d. 17.5

D A

BC

57 °

R

S

T

Q

1

31°3

2

4

____ 23. Find AB.

a. 21.5 c. 8

b. 11 d. 5

____ 25. A scenic overlook which extends over a ravine is shaped like a kite.

Find .

a. 40° c. 104°

b. 112° d. 208°

____ 26. Name the quadrilateral with the most specific name that will describe it.

a. Square c. isosceles trapezoid

b. parallelogram d. rectangle

A

D

B

C

M

N

2716

W

X

Y

Z

112°

40°

24

24

75°

105°

____ 27. . What additional condition(s) would make quadrilateral ABCD a parallelogram?

a.

c.

b. d.

____ 28. Decide whether quadrilateral with vertices , , , and is a rectangle,

rhombus, square, or parallelogram.

a. square c. parallelogram

b. rectangle d. rhombus

____ 31. Quadrilateral ABCD is a kite. What conditions must be true?

a. no parallel sides c. diagonals are perpendicular

b. opposite sides are congruent d. 2 pair congruent sides

Match the angle measure below to its regular polygon.

a. Nonagon d. Dodecagon

b. Heptagon e. Decagon

c. Octagon f. Hexagon

____ 32. Exterior angle of 30°

____ 33. Exterior angle of 51.4°


A B

CD

F

A

B

C

D

2 4–2–4 x

2

4

–2

–4

y


Match the given side or angle to its measure using the parallelogram below.

a. 94 e. 150

b. 22 f. 26

c. 24 g. 60

d. 75 h. 300

____ 36. Find BFC.

____ 37. Find BCD.

____ 38. Find CD.

____ 39. Find AC.

40. Find the measures of all the interior angles.

41. A student had this question on a recent Geometry test: If , ,

, and ; find the values of x and y that make quadrilateral ABCD a

parallelogram. The student’s answer was , . The teacher, marked the student’s answer incorrect.

The student insists it is correct and would like the teacher to take another look at it. Is the teacher correct in

scoring this answer as incorrect? Explain.

A B

CD

79°

F13 22

24

33

86°

6x°

3x°

4x°7x°

7x°

46. In rectangle ABCD, , , and . Find the value of y.

47. List all of the special quadrilaterals that quadrilateral ABCD must be with each listed property: parallelogram,

rectangle, rhombus, square, or none. Draw a counterexample if none.

51. In quadrilateral ABCD, , , , and .

a. Find , , , and .

b. Classify quadrilateral ABCD as a kite, trapezoid, or isosceles trapezoid. Justify your answer.

c. What is true of the side lengths?

State which theorem you can use to show that the quadrilateral is a parallelogram.

____ 57.

a. Parallelogram Opposite Sides Converse c. Opposite Sides Parallel and Congruent

Theorem

b. Parallelogram Opposite Angles Converse d. Parallelogram Diagonals Converse

____ 58.


Theorem


A B

D C

P

____ 59.


Theorem


____ 60.


Theorem


____ 61.


Theorem


Classify the special quadrilateral.

____ 62.

a. rhombus

b. rectangle

c. square

71. For any rhombus ABCD, is it always or sometimes true that ? Explain your reasoning.

72. For any rhombus EFGH, is it always or sometimes true that ? Explain your reasoning.

73. For any rectangle PQRS, is it always or sometimes true that ? Explain your reasoning.

74. For any rectangle EFGH, is it always or sometimes true that ? Explain your reasoning.

75. For any rectangle ABCD, is it always or sometimes true that ? Explain your reasoning.

83. Find the number of sides a regular polygon must have so each interior angle measure is 150°. Justify your

answer.

88. Find the number of sides a regular polygon must have so each interior angle measure is 162°. Justify your

answer.

89. Find the number of sides a regular polygon must have so each interior angle measure equals each exterior

angle measure. Justify your answer.

90. Prove than an equilateral polygon is not necessarily a regular polygon by providing a counterexample.

91. Find the number of sides a regular polygon must have so each interior angle measure is four times the

measure of each exterior angle. Justify your answer.

____ 93. The triangles are similar. Find the value of x.

a. 16 c. 18

b. 14 d. 24

A

B

C

R

T

S

x

2430

24

32

40

____ 95. . Find the length of median .

a. 33 c. 24

b. 36 d. 54

____ 97. A rectangular yard is fenced in using 319 feet of custom fence. Your friends really like the fence and decide

to fence in their yard using the same fence. Their yard is similar but has a scale factor of times the size of

yours, how much fence, to the nearest foot, will they have to purchase?

a. 321 feet c. 510 feet

b. 542 feet d. 199 feet

____ 99. . The area of is given. Find the area of .

a. 1152 in. c. 240 in.

b. 48 in. d. 25 in.

____100. . The area of QRST is given. Find the area of WXYZ.

A B

C

P

D

F

EQ

18 18

24 24

27

8

5

A

B

C D FD

E

12

60

A = 1200 sq in.

Q

R

T

S X Y

W Z

8

24

A = 144 sq in.

____101. Two trees are growing in a clearing. The first tree is 17 feet tall and casts a 10 foot shadow. The second tree

casts a 35 foot shadow. How tall is the second tree to the nearest tenth of a foot?

a. about 72.1 ft c. about 4.9 ft

b. 42 ft d. 59.5 ft

____103. What is the length of ?

a. 15 c. 57

b. 19 d. 21

____105. Find the value of x.

a. 11 c. 19.3

b. 10.5 d. 15


a. 39.5 c. 40

b. 75 d. 42.5

A

B

C

F G

63 57

21

x

21

25

35

17

37.5

x

52.5


a. 14 c. 20

b. 11 d. 18

____108. Select the valid similarity statement(s).

a. c. b. d.

____109. Which triangles are similar to ?

a. c. b. d.

11

x

22

21

P

F

M

B

TI82°

82°

C

A

F

GB

ED

H

8 8

28 28

109

16.2 18

6

10.8

69° 67°

44°

Match the segments below to the correct length when ?

a. 18 d. 42

b. 22.5 e. 8

c. 12 f. 36

____110. BF

____111. FK

____112. AC

113. In the diagram, . Find the scale factor. Then list all pairs of congruent angles and write the

ratios of the corresponding side lengths in a state of proportionality.

114. In the diagram, . Find the scale factor. Then list all pairs of congruent angles and write the

ratios of the corresponding side lengths in a state of proportionality.

A

B

C

F G

13.5

36 27

N

K

24

F

Q

F XX24

28 36

C IC

V

30

35 45

D

X

F

V

F

V

36

3228

40 N

K

I

O

K

45

50

40

35

118. with side lengths as labeled and ,

a. Find AF.

b. Find the perimeter of .

c. Find the area of .

119. Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

120. Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

C

A

E

DB

F

G

108

15

K

B

F

E

H O

49°

43°

P Q

R

G

H

K

21°

21°

78°

80°

125. Find the value of x that makes .

127. Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the

scale factor from triangle 2 to triangle 1.

____133. A castle guard is standing on the opposite side of an 8-foot moat and wants to reach a window that is 15 feet

above the ground. The guard props a ladder against the castle wall to form a right triangle as shown.

Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot.

a. 17.0 ft c. 289.0 ft

b. 23.0 ft d. about 12.7 ft

A

B

A CC25

2x + 6 40

R S

T

x + 18

36 48

A

B

C

W

X

Y

71°

71°

8

18

10

27

1

2

Not drawn to scale

8 ft

15 ft

____136. In the diagram, BC = 12 . Find AB. Write your answer in simplest form.

____137. In the diagram, and . Find AB. Write your answer in simplest form.

____140. In the diagram, 12. Find AC and BC. Write your answers in simplest form.

2

°

2 2

°

°

____141. In the diagram, . Find BC and AB. Write your answers in simplest form.

____142. A chemistry teacher makes a sign for the door to the room that contains the chemicals used in class. The

danger sign is shaped like an equilateral triangle. Estimate the area of the sign to the nearest tenth of a square

inch.

a. about 70.1 in. c. about 140.3 in.

b. about 280.6 in. d. about 54.0 in.

____145. Find the geometric mean of 4 and 8.

a. 16 c.

b. d.

Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth.

12 3

°

°

18 in.

4 2

4 5 2 3

____146.

____147.

a. 11.6 c. 3.8

b. 26.4 d. 1.7

____149.

a. , c. ,

b. , d. ,

____150.

a. , c. ,

b. , d. ,

8

10

z

x

11

19 °

x

y

57°32

x

7

33°

y

____151.

a. 6.9 c. 3.3

b. 4.8 d. 6.2

Find the exact value of the variable.

____152.

a. c.

b. d. 4.5

____157. In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit.

The zip line extends from the top of a tower to a point on the ground 48.2 feet away from the base of the

tower. The angle of elevation of the zip line is 33°. Estimate the length of the zip line to the nearest tenth of a

foot.

6

8

10

x

1

9

x

3 10

82

Not drawn to scale

48.2 ft33°


b. about 31.3 ft d. about 57.5 ft

____159. Write in terms of cosine.

a. c. b. d.

____160. Write in terms of sine.

a. c. b. d.

____161. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25°.

When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your

answer to the nearest tenth of a foot.


b. about 82.8 ft d. about 126.8 ft

Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of

a degree.

____163.

a. about 58.0° c. about 1.0°

b. about 49.4° d. about 32.0°

____164.



Solve the triangle. Round decimal answers to the nearest tenth.

____166.

a. , , c. , ,

b. , , d. , ,

x

y

11

FH

G

59°

168.

170.

171.

A

B

C

70°14

24

A

B

C

69°

33°

8

B

A

C

27°

30°

24

172.

173.

174.

Use a calculator to find the trigonometric ratio. Round your answer to four decimal places.

____176. tan 106°

a. about 1.5706 c. about –3.4874

b. about 1.5614 d. about –1.0592

A

B

C38°

27

31

117°16

39C

B

CA

B

A

C

29

18

35

____177. cos 145°

a. about 0.8192 c. about 0.8839

b. about –0.8839 d. about –0.8192

____178. sin 152°

a. about –0.9333 c. about –0.4695

b. about 0.4695 d. about 0.9333

____179. Find the area of the triangle. Round your answer to the nearest tenth.

a. about 503.0 units2 c. about 258.8 units2

b. about 234.6 units2 d. about 555.0 units2

____181. You plan to install a sprinkler system in your yard. You designate one sprinkler head to lie on a vertex of a

triangular garden with dimensions of 34 feet, 19 feet, and 43 feet. The sprinkler heads are ordered according

to the angle through which they rotate. What is the largest angle of rotation you can order?

a. 155° c. 50°

b. 26° d. 105°

____187. Use a special right triangle to find the tangent of a 30 angle.

a. b. 2 c.

d.

____189. Use a special right triangle to find the tangent of a 45 angle.

A

BC

25°

3037

a. b. 1 c.

d. 2

____190. Use a special triangle to find the sine of a 45 angle.

a. b.

c.

d.

____193. Use a special triangle to find the cosine of a 30 angle.

a.

b.

c.

d.

____194. Use a special triangle to find the sine of a 60 angle.

a.

b.

c.

d.

____196. In , , , and . Which statements are true?

a. c. b. d.

____197. Which statements are true about ?

a. c. b. d.

____198. Which measures are angle measures of ?

145

G

H

F

15

36

39

FH

G



____199. Which ratios have the same value as cos P?

a. sin P c. tan P

b. sin Q d. cos Q

____200. Which ratios are equal to ?

a. tan R c. tan S

b. cos S d. sin R

Match the statement below with the set of segment lengths it describes. Use each set of segment

lengths only once.

a. 10, 7, d. 6, 5,

C

A

B

35

25

29

658 119

b. 6, 6, e. 7, 24, 25

c. 6, 7,

____204. The segment lengths form a right triangle.

____205. The segment lengths form an acute triangle.

____206. The segment lengths form an obtuse triangle.

____207. The segment lengths do not form a triangle.

____208. The segment lengths form a Pythagorean triple.

Use to match the measure below with its approximate value.

a. about 15.3 d. about 15.8

b. about 74.2 e. about 74.7

c. about 22.8

____212. FH

____213.

____214.

215. Find the value of x. Then tell whether the side lengths form a Pythagorean triple.

38

85

6

22G

H

F

1

15

x

219. In the diagram, , , and .

223. Find , , , and cos F. Write each answer as a fraction and as a decimal rounded to four places.

226. Determine which of the two acute angles has a sine of .

13 194

Not drawn to scale

B

A

C

16

30

34

G

FH

9

41

18

80

82

G

F

H

227. In , , , and . Determine which of the acute angles has a cosine of

0.2400.

230. Find the value of each variable. Round your answers to the nearest tenth. How does compare to

? Justify your answer.

589

FH

G

6

7

w°

x°

y°

z°

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FINAL EXAM Review Chapters 7,8,9. · 2016-05-16 · FINAL EXAM Review Chapters 7,8,9. ____ 1. Find the sum of the measures of the interior angles of a convex hexagon. ... Estimate