GEOM



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 [pic] inches and the width is [pic] 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 [pic], which equation must be true?

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 4. If [pic], then [pic] = ____.

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

Solve the proportion.

____ 5. [pic]

|a. |[pic] |b. |5 |c. |[pic] |d. |25 |

____ 6. [pic]

|a. |–3 |b. |[pic] |c. |[pic] |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 [pic] for x and y with x > 0 and y > 0.

|a. |x = 6; y = 6 |c. |x = 3; y = 12 |

|b. |x = 2; y = 18 |d. |x = 8; y = 24 |

____ 10. [pic]. Complete the statements.

[pic]

|a. |[pic][pic] |

|b. |[pic] |

|a. |[pic]; DC |b. |E; AE |c. |E; DC |d. |[pic]; AE |

____ 11. Figure [pic]. Name a pair of corresponding sides?

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 12. The two rectangles are similar. Which is a correct proportion for corresponding sides?

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 13. Determine whether the figures are similar.

[pic]

|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.

____ 14. In ΔRST, RS = 10, RT = 15, and m∠R = 32. In ΔUVW, UV = 12, UW = 18, and m∠U = 32.

|a. |[pic]; [pic] |c. |[pic]; [pic] |

|b. |[pic]; [pic] |d. |The triangles are not similar. |

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

____ 15. [pic][pic]

|a. |x = [pic], y = [pic] |c. |x = 9, y = [pic] |

|b. |x = [pic], y = 27 |d. |x = 9, y = 27 |

____ 16. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

[pic]

|a. |AB = 2; EF = 10 |c. |AB = 20; EF = 4 |

|b. |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 [pic] in. by 11 in. What are the dimensions of the largest complete enlargement you can make?

|a. |[pic] in. [pic][pic] in. |c. |[pic][pic] in. |

|b. |[pic] in. [pic][pic] in. |d. |[pic][pic] 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.

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 21. Are the triangles similar? If so, explain why.

[pic]

|a. |yes, by SAS |b. |yes, by SSS |c. |yes, by AA |d. |no |

____ 22. Which group contains triangles that are all similar?

|a. |[pic] |

|b. |[pic][pic] |

|c. |[pic] |

|d. |[pic] |

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

____ 23. In ΔQRS, QR = 16, RS = 64, and m∠R = 29. In ΔUVT, VT = 8, TU = 32, and m∠T = 29.

|a. |[pic]; ASA |c. |[pic]; ASA |

|b. |[pic]; ASA |d. |The triangles are not similar. |

____ 24. [pic][pic]

|a. |[pic]; SSS |c. |[pic]; AA |

|b. |[pic]; SAS |d. |The triangles are not similar. |

____ 25. [pic]

|a. |[pic]; SAS |c. |[pic]; SSS |

|b. |[pic]; SAS |d. |The triangles are not similar. |

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

____ 26. [pic]

|a. |SSS Postulate; [pic] |c. |SAS Postulate; [pic] |

|b. |AA Postulate; [pic] |d. |AA Postulate; [pic] |

____ 27. [pic]

|a. |SSS Postulate; [pic] |c. |SAS Postulate; [pic] |

|b. |AA Postulate; [pic] |d. |AA Postulate; [pic] |

____ 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.

[pic]

|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.

[pic]

|a. |20 ft |b. |38.4 ft |c. |55 ft |d. |25 ft |

____ 30. Use the Side-Splitter Theorem to find x, given that [pic].

[pic]

|a. |12 |b. |6 |c. |20 |d. |24 |

____ 31. Given [pic], solve for x.The diagram is not drawn to scale.

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

Solve for x.

____ 32. [pic]

|a. |5 |b. |2.5 |c. |7.5 |d. |10 |

____ 33. [pic]

|a. |8 |b. |12 |c. |6 |d. |2 |

____ 34. [pic] bisects [pic] , LM = 18, NO = 4, and LN = 10. Find OM.

[pic]

|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 cm |

|b. |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 [pic] then 3a = ____.

Solve the proportion.

38. [pic]

39. [pic]

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 ΔQRS, QR = 4, RS = 15, and m∠R = 36. In ΔUVT, VT = 8, TU = 32, and m∠T = 36.

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

[pic]

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

44. The pentagons are regular.

[pic]

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. [pic] What is the measure of [pic]?

[pic]

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

[pic]

49. Given: [pic]. Find the length of [pic]. The diagram is not drawn to scale.

[pic]

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:

[pic]

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:

[pic]

46. ANS:

801 cm[pic]

47. ANS:

70°

48. ANS:

80 ft

49. ANS:

9

50. ANS:

x = 10; y = 25.5

51. ANS:

[pic]

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.

[pic] inches.

Your canvas should be about 18 in. by 29 in.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download