Name: Per: Date:--------------------------------- ----- ---------- ID: A

Geometry Chapter 7 Review

Multiple ChoiceIdentify the letter of 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?

4ml __12 m 8ml

x

12 X 12 x 4 XB. -- C. -- - D. -- -4 8 4 20 12 8

12 xA.8 4

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

2. In D.RST,RS= 10, RT= 15, and mLR = 32. In i1UVW, UV= 12, UW= 18, and mLU= 32.5 6

A. MST - !1WUV· - C. MST - !1VWU· -, 6 ' 5

5B. MST - i1UVW· - D. The triangles are not similar.,6

3. Given: PQ II Be. Find the length of AQ. The diagram is not drawn to scale.

A

14

BA. 9

CB. 10 c. 14 D. 7

ID: A

4. Michele wanted to measure the height of her school's flagpole. She placed a mirror on the ground 48 feetfrom the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyeswere 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height ofthe flagpole to the nearest tenth of a foot.

5ft...L.

A. 20 ft B. 38.4 ft C. 55 ft D. 25 ft

State whether the triangles are similar. If so, write a similarity statement and the postulate or theoremyou used.

5.

B

A cA. MDB ~ /)"CDB; SAS SimilarityB. MBD ~ /)"CDB; SAS Similarity

C. M.DB ~ /)"CDB; SSS SimilarityD. The triangles are not similar.

6. In /)"QRS, QR = 16, RS= 64, and mLR = 29. In /)"UVT, VT= 8, TU= 32, and mLT= 29.A. MRQ ~ /)"UTV; SSS Similarity C. /)"RSQ ~ /)"TUV; AA SimilarityB. /)"QRS ~ /)"VTU; SAS Similarity D. The triangles are not similar.

Solve the proportion.

4 167.

a 36A. 16 B. 9 C. 36 D. 144

2

ID: A

n-6 n-58. =

3n 3n + 12 9A. -3 B. - C. - D. 35 17

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

9. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

A

D

5~

E x F

B 4 CA. AB = 2; EF = 10B. AB=10;EF=2

C. AB=20;EF=4D. AB=4;EF=20

Solve forx.

10.

x-2

x+l

A. 5 B. 2.5 C. 7.5 D. 10

3

ID: A

11.

A. 8 B. 12 C. 6 D. 2

12.

52A.3

3B.

4C. 17

52D.

7

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

13.

Not drawn to scale

A. SAS Similarity; IIIB. SSS Similarity; 3~

C. AA Similarity; 3~

D. AA Similarity; III

4

ID: A

14. Given AE II BD, solve for x.The diagram is not drawn to scale.A

E 5 D 7 c

6A. 7-

7

2B. 3-

11

2C. 15-

5

2D. 26-

5

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

ODD000000000000000000DO ::::) DO

160

120 ft

A. 80 ft B. 264 ft C. 60 ft D. 72 ft

16. Find the ratio of the perimeter of the larger rectangle to the perimeter ofthe smaller rectangle.NOTE: The rectangles are NOT similar.

5ft 13 ft9ft

11 ft

4 3 5 11A. B. - C. D.

3 4 3 9

5

ID: A

__ 17. Are the triangles similar? If so, explain why.

A. yes, by SAS B. yes, by SSS C. yes, by AA D. no

18. A model is made of a car. The car is 9 feet long and the model is 7 inches long. What is the ratio of the lengthof the car to the length of the model? IJ.,.WA. 9: 7 B. 7: 9 C. 7: 108 D. 108: 7 t s~rfs .

19. Write a similarity statement for the triangles.D

G

/\ 67"

~C E F H

A. !1CDE - MHGB. !1CED - MGH

C. !1CDE - MGHD. !1EDC - MGH

6

ID: A

20. Determine whether the figures are similar.

7.2

5.15.1

7.2

Not drawn to scale

A. similarB. not similarC. not enough information

21. a 3If - = - then 4a =

b 4'A. 8b B. 3b C. 6b D. 4b

22. ABCD ~ WXYZ AD = 8, DC = 2, and WZ = 44. Find YZ The figures are not drawn to scale.X

B

AVe w yD

ZA. II B. 88 C. 26 D. 176

23. Find x to the nearest tenth.

Not drawn to scale

A. 4.8 B. 14.4 C. 9.4 D. 1.7

7

ID: A

24. A map of Australia has a scale of 1 em to 120 km. If the distance between Melbourne and Canberra is 463km, how far apart are they on the map, to the nearest tenth of a centimeter?A. 0.4 em B. 3.9 em C. 38.6 em D. 55,560 em

25. A model is built having a scale of 1 : 100,000. How high would a 35,600-ft mountain be in the model? Giveyour answer to the nearest tenth of an inch.A. 4.272 in. B. 2.136 in. C. 0.356 in. D. 427,200 in.

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