GEOM. CH. 7 TEST REVIEW - SIMILARITY
MultipleChoice
Identify the choice that best completes the statement or answers the question.
____ 1. 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?
a. / 1 : 725 / b. / 725 : 1 / c. / 12 : 725 / d. / 725 : 12____ 2. The length of a rectangle is inches and the width is inches. What is the ratio, using whole numbers, of the length to the width?
a. / 26 : 15 / b. / 26 : 30 / c. / 15 : 26 / d. / 13 : 15____ 3. If , which equation must be true?
a. / / b. / / c. / / d. /____ 4. If , then = ____.
a. / / b. / / c. / / d. /Solve the proportion.
____ 5.
a. / / b. / 5 / c. / / d. / 25____ 6.
a. / –3 / b. / / c. / / d. / 3____ 7. On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long and 4 cm wide on the blueprint?
a. / 22.5 ft / b. / 1.5 ft / c. / 6 ft / d. / 16.5 ft____ 8. 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.
____ 9. Solve the extended proportion for x and y with x > 0 and y > 0.
a. / x = 6; y = 6 / c. / x = 3; y = 12b. / x = 2; y = 18 / d. / x = 8; y = 24
____ 10. . Complete the statements.
a. /b. /
a. / ; DC / b. / E; AE / c. / E; DC / d. / ; AE
____ 11. Figure . Name a pair of corresponding sides?
a. / / b. / / c. / / d. /____ 12. The two rectangles are similar. Which is a correct proportion for corresponding sides?
a. / / b. / / c. / / d. /____ 13. Determine whether the figures are similar.
a. / similarb. / not similar
c. / not enough information
Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.
____ 14. In DRST, RS = 10, RT = 15, and mÐR = 32. In DUVW, UV = 12, UW = 18, and mÐU = 32.
a. / ; / c. / ;b. / ; / d. / The triangles are not similar.
The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
____ 15.
a. / x = , y = / c. / x = 9, y =b. / x = , y = 27 / d. / x = 9, y = 27
____ 16. Triangles ABC and DEF are similar. Find the lengths of AB and EF.
a. / AB = 2; EF = 10 / c. / AB = 20; EF = 4b. / AB = 10; EF = 2 / d. / AB = 4; EF = 20
____ 17. You want to draw an enlargement of a design that is printed on a card that is 4 in. by 5 in. You will be drawing this on an piece of paper that is in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
a. / in. in. / c. / in.b. / in. in. / d. / in.
____ 18. An artist’s canvas forms a golden rectangle. The longer side of the canvas is 33 inches. How long is the shorter side? Round your answer to the nearest tenth of an inch.
a. / 20.4 in. / b. / 53.4 in. / c. / 16.5 in. / d. / 66 in.____ 19. If one measurement of a golden rectangle is 8.8 inches, which could be the other measurement?
a. / 14.238 in. / b. / 10.418 in. / c. / 7.182 in. / d. / 1.618 in.____ 20. Write a similarity statement for the triangles.
a. / / c. /b. / / d. /
____ 21. Are the triangles similar? If so, explain why.
a. / yes, by SAS / b. / yes, by SSS / c. / yes, by AA / d. / no____ 22. Which group contains triangles that are all similar?
a. /b. /
c. /
d. /
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
____ 23. In DQRS, QR = 16, RS = 64, and mÐR = 29. In DUVT, VT = 8, TU = 32, and mÐT = 29.
a. / ; ASA / c. / ; ASAb. / ; ASA / d. / The triangles are not similar.
____ 24.
a. / ; SSS / c. / ; AAb. / ; SAS / d. / The triangles are not similar.
____ 25.
a. / ; SAS / c. / ; SSSb. / ; SAS / d. / The triangles are not similar.
Explain why the triangles are similar. Then find the value of x.
____ 26.
a. / SSS Postulate; / c. / SAS Postulate;b. / AA Postulate; / d. / AA Postulate;
____ 27.
a. / SSS Postulate; / c. / SAS Postulate;b. / AA Postulate; / d. / AA Postulate;
____ 28. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale.
a. / 42.3 m / b. / 47.4 m / c. / 73.8 m / d. / 82.8 m____ 29. 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.
a. / 20 ft / b. / 38.4 ft / c. / 55 ft / d. / 25 ft____ 30. Use the Side-Splitter Theorem to find x, given that .
a. / 12 / b. / 6 / c. / 20 / d. / 24____ 31. Given , solve for x.The diagram is not drawn to scale.
a. / / b. / / c. / / d. /Solve for x.
____ 32.
a. / 5 / b. / 2.5 / c. / 7.5 / d. / 10____ 33.
a. / 8 / b. / 12 / c. / 6 / d. / 2____ 34. bisects , LM = 18, NO = 4, and LN = 10. Find OM.
a. / 7.2 / b. / 45 / c. / 5.43 / d. / 2.22____ 35. An angle bisector of a triangle divides the opposite side of the triangle into segments 8 cm and 4 cm long. A second side of the triangle is 4.4 cm long. Find all possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter.
a. / 32 cm, 2.2 cm / c. / 8.8 cm, 35.2 cmb. / 8.8 cm, 2.2 cm / d. / 35.2 cm, 7.3 cm
ShorShort Answer
36. 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?
37. If then 3a = ____.
Solve the proportion.
38.
39.
40. A map of Australia has a scale of 1 cm to 120 km. If the distance between Melbourne and Canberra is 463 km, how far apart are they on the map, to the nearest tenth of a centimeter?
41. A model is built having a scale of 1 : 100,000. How high would a 35,600-ft mountain be in the model? Give your answer to the nearest tenth of an inch.
Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.
42. In DQRS, QR = 4, RS = 15, and mÐR = 36. In DUVT, VT = 8, TU = 32, and mÐT = 36.
43. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.
The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
44. The pentagons are regular.
45. 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?
46. If the long side of a golden rectangle is 36 cm, what is its area? Round your answer to the nearest tenth.
47. What is the measure of ?
48. Use the information in the diagram to determine the height of the tree to the nearest foot.
49. Given: . Find the length of . The diagram is not drawn to scale.
53. Explain how you would decide the size of your canvas should be if you want it in the shape of a golden rectangle.
AN
1. ANS: A
2. ANS: A
3. ANS: B
4. ANS: C
5. ANS: D
6. ANS: A
7. ANS: A
8. ANS: B
9. ANS: C
10. ANS: A
11. ANS: D
12. ANS: B
13. ANS: B
14. ANS: B
15. ANS: D
16. ANS: B
17. ANS: D
18. ANS: A
19. ANS: A
20. ANS: C
21. ANS: C
22. ANS: A
23. ANS: D
24. ANS: A
25. ANS: A
26. ANS: D
27. ANS: B
28. ANS: A
29. ANS: A
30. ANS: A
31. ANS: A
32. ANS: A
33. ANS: A
34. ANS: A
35. ANS: B
36. ANS:
18 : 1
37. ANS:
5b
38. ANS:
9
39. ANS:
40. ANS:
3.9 cm
41. ANS:
4.272 in.
42. ANS:
The triangles are not similar.
43. ANS:
29.5
44. ANS:
x = 27, y = 4
45. ANS:
46. ANS:
801 cm
47. ANS:
70°
48. ANS:
80 ft
49. ANS:
9
50. ANS:
x = 10; y = 25.5
51. ANS:
52. ANS:
14.4
OTHER
53. ANS:
Answers may vary. Sample: Golden rectangles are in the ratio of about 1.618 : 1. So if you choose the length of the shorter side to be, let’s say, 18 inches, you could set up a proportion.
inches.
Your canvas should be about 18 in. by 29 in.