Geometry Chapter 7 Test REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. 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? a. 18 : 1 b. 1 : 18 c. 9 : 6 d. 6 : 9

____

2. If

then 3a = ____.

a. 3b

b. 10b

c. 5b

d. 6b

a. 54

b. 81

c. 9

d. 18

a.

b. 5

c. 1

d. 25

Solve the proportion. ____

____

3.

4.

1 25

____

5. You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your scale drawing? a. 24 in. by 144 in. c. 24 in. by 10 in. b. 16 in. by 10 in. d. 16 in. by 144 in.

____

6.

. Complete the statements. A

G

E

B

F

H

D

J

C

a.

b.

GH



AB

DJ a.

; DC

b. E; AE

c. E; DC

d.

; AE

____

7. The two rectangles are similar. Which is a correct proportion for corresponding sides? 4m 8m 12 m x

b.

a.

____

c.

d.

8. Determine whether the figures are similar. 7.5

3

1.5

3

4.65 4.65

7.5

1.5 Not drawn to scale

a. similar b. not similar c. not enough information Are the polygons similar? If they are, write a similarity statement and give the similarity ratio. ____

9. In RST, RS = 10, RT = 15, and mR = 32. In UVW, UV = 12, UW = 18, and mU = 32. a. c. ; ; b.

;

d. The triangles are not similar.

____ 10. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36. a. c. ; ; b.

;

d. The triangles are not similar.

____ 11. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.

X B W

A

Y

C D Z

a. 118

b. 29.5

c. 21.7

d. 177

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y. ____ 12.

a. b.

c.

x=

,y=

x=

, y = 27

x = 9, y =

d. x = 9, y = 27

____ 13. The pentagons are similar. Find the value of the variables. x– 3

8

y–2

2.5

4 16

a. x = 13, y = 4 b. x = 7, y = 2

c. x = 5.5, y = 10 d. x = 13, y = 6

____ 14. Triangles ABC and DEF are similar. Find the lengths of AB and EF. A D

5x

5

E x F B

4

C

a. AB = 2; EF = 10 b. AB = 10; EF = 2

c. AB = 20; EF = 4 d. AB = 4; EF = 20

____ 15. You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page? a. c. d.

b.

____ 16. Write a similarity statement for the triangles. D

53°

G

60°

67°

60°

C

E

F

H

c. d.

a. b. ____ 17. Are the triangles similar? If so, explain why.

30.4°

84.6°

84.6°

b. yes, by SSS

a. yes, by SAS ____ 18.

65°

What is the measure of

c. yes, by AA

d. no

c. 250

d. 35

?

R )

U )

47° 63° )) Q

a. 70

))

S

T

V

b. 110

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. ____ 19. In QRS, QR = 16, RS = 64, and mR = 29. In UVT, VT = 8, TU = 32, and mT = 29.

a. b.

c. ; ASA d. The triangles are not similar.

; ASA ; SAS

____ 20.

B

O

5

M

12

5 7.5

8

A

7.5

C N

; SSS ; SAS

a. b.

c. ; AA d. The triangles are not similar.

Explain why the triangles are similar. Then find the value of x. ____ 21.

)

x 7

)

12 8 Not drawn to scale

a. b.

SSS AA

1 2 1 Postulate; 10 2 Postulate; 10

c. d.

SAS AA

2 3 2 Postulate; 4 3 Postulate; 4

____ 22. 6 8

>

4 >

x

Not drawn to scale

a.

1 3 b. 1 AA Postulate; 13 3 SSS Postulate; 5

c. d.

SAS Postulate; 13 AA Postulate; 5

1 3

1 3

____ 23. Use the information in the diagram to determine the height of the tree to the nearest foot.

a. 80 ft

b. 264 ft

c. 60 ft

d. 72 ft

Find the geometric mean of the pair of numbers. ____ 24. 175 and 7 a. 55

b. 45

c. 35

____ 25. 5 and 6 a. 30

b. 6

c.

d. 40 d.

35

30

Solve for a and b. ____ 26.

)

8

10 6

a

) b

____ 27.

a.

c.

b.

d.

Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

7

a. 28

21

b. 7 3

c. 147

____ 28. Use the Side-Splitter Theorem to find x, given that

d. 2 7 .

A

8 P

12 Q

18

x B

C

a. 12

b. 6

____ 29. Given:

c. 20

. Find the length of

d. 24

. The diagram is not drawn to scale.

A

6 P

Q

12

18

B

C

a. 11

b. 12

c. 18

d. 9

b. 12

c. 6

d. 2

b. 24

c. 2 6

d.

Solve for x. ____ 30.

> 24

36

x

> 12 >

a. 8 ____ 31. x 3

8 Not drawn to scale

a. 11

____ 32. Find x to the nearest tenth.

33

8.3

x

)) ))

6.7

11.6

Not drawn to scale

a. 4.8

b. 14.4

c. 9.4

d. 1.7

Geometry Chapter 7 Test REVIEW Answer Section MULTIPLE CHOICE 1. ANS: OBJ: NAT: KEY: 2. ANS: OBJ: NAT: KEY: 3. ANS: OBJ: NAT: KEY: 4. ANS: OBJ: NAT: KEY: 5. ANS: OBJ: NAT: KEY: 6. ANS: OBJ: NAT: TOP: 7. ANS: OBJ: NAT: TOP: 8. ANS: OBJ: NAT: TOP: 9. ANS: OBJ: NAT: TOP: KEY: 10. ANS: OBJ: NAT: TOP: KEY: 11. ANS: OBJ:

A PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-1 Example 1 ratio | word problem C PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-1 Example 2 proportion | Cross-Product Property C PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-1 Example 3 proportion | Cross-Product Property D PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-1 Example 3 proportion | Cross-Product Property B PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-1 Example 4 proportion | Cross-Product Property | word problem A PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 7-2 Example 1 KEY: similar polygons B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 7-2 Example 1 KEY: similar polygons | corresponding sides B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 7-2 Example 2 KEY: similar polygons B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 7-2 Example 2 similar polygons | corresponding sides | corresponding angles D PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 7-2 Example 2 similar polygons | corresponding sides | corresponding angles B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-2 Example 3 KEY: corresponding sides | proportion ANS: D PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: 7-2.1 Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-2 Example 3 KEY: corresponding sides | proportion ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: 7-2.1 Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-2 Example 3 KEY: corresponding sides | proportion ANS: B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons OBJ: 7-2.1 Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-2 Example 3 KEY: corresponding sides | proportion | similar polygons ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar Polygons OBJ: 7-2.2 Applying Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 TOP: 7-2 Example 4 KEY: similar polygons | word problem ANS: C PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 1 KEY: Angle-Angle Similarity Postulate ANS: C PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 2 KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 1 KEY: Angle-Angle Similarity Postulate | corresponding angles ANS: B PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 2 KEY: corresponding sides ANS: A PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 2 KEY: Side-Side-Side Similarity Theorem ANS: D PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.2 Applying AA, SAS, and SSS Similarity NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 3 KEY: Angle-Angle Similarity Postulate ANS: B PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.2 Applying AA, SAS, and SSS Similarity NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 TOP: 7-3 Example 3 KEY: Angle-Angle Similarity Postulate ANS: A PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.2 Applying AA, SAS, and SSS Similarity

24.

25.

26.

27.

28.

29.

30.

31.

32.

NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP: ANS: OBJ: NAT: TOP:

NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.3 | MI G2.3.4 7-3 Example 4 KEY: Angle-Angle Similarity Postulate | word problem C PTS: 1 DIF: L2 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.4 7-4 Example 1 KEY: geometric mean | proportion D PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.4 7-4 Example 1 KEY: geometric mean | proportion A PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.4 7-4 Example 2 KEY: corollaries of the geometric mean | proportion B PTS: 1 DIF: L2 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.4 7-4 Example 2 KEY: corollaries of the geometric mean | proportion A PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles 7-5.1 Using the Side-Splitter Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 STA: MI G2.3.4 7-5 Example 1 KEY: Side-Splitter Theorem D PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles 7-5.1 Using the Side-Splitter Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 STA: MI G2.3.4 7-5 Example 1 KEY: Side-Splitter Theorem A PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles 7-5.1 Using the Side-Splitter Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 STA: MI G2.3.4 7-5 Example 2 KEY: corollary of Side-Splitter Theorem D PTS: 1 DIF: L2 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MI G2.3.4 7-4 Example 2 KEY: corollaries of the geometric mean | proportion B PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles 7-5.2 Using the Triangle-Angle-Bisector Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 STA: MI G2.3.4 7-5 Example 3 KEY: Triangle-Angle-Bisector Theorem