Name: ________________________ Class: ___________________ Date: __________ ID: A Chapter 7 review Multiple Choice Identify the choice that best completes the statement or answers the question. x+3 = y+2 1. If ____ d. y − 1 3 2 2. The two rectangles are similar. Which is a correct proportion for corresponding sides? 3 y+1 a. 12 a. ____ 2 , then x ____ = 3 b. x b. = ____. y c. 12 = x c. y 12 = x d. 4 = x 8 4 4 8 4 20 12 8 3. 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. Short Answer 4. A model is made of a car. The car is 3 meters long and the model is 5 centimeters long. What is the ratio of the length of the car to the length of the model? 5. If a = b 4 5 , then 5a = ____. Solve the proportion. 6. 7. 8 = a 16 18 n−6 3n = n−5 3n + 1 8. On a blueprint, the scale indicates that 9 cm represent 13 feet. What is the length of a room that is 9.9 cm long and 6 cm wide on the blueprint? 9. You want to produce a scale drawing of your living room, which is 26 ft by 18 ft. If you use a scale of 2 in. = 4 ft, what will be the dimensions of your scale drawing? 10. Solve the extended proportion x 9 = 4 y = y 36 for x and y with x > 0 and y > 0. 1 Name: ________________________ ID: A Are the polygons similar? If they are, write a similarity statement and give the similarity ratio. 11. In ∆RST, RS = 10, RT = 15, and m∠R = 32. In ∆UVW, UV = 12, UW = 18, and m∠U = 32. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y. 12. 13. Triangles ABC and DEF are similar. Find the lengths of AB and EF. 14. An artist’s canvas forms a golden rectangle. The longer side of the canvas is 36 inches. How long is the shorter side? Round your answer to the nearest tenth of an inch. 15. If the long side of a golden rectangle is 21 cm, what is its area? Round your answer to the nearest tenth. 16. Are the triangles similar? If so, explain why. 2 Name: ________________________ ID: A State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. 17. 18. Explain why the triangles are similar. Then find the value of x. 19. 20. 3 Name: ________________________ ID: A 21. 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. Find the geometric mean of the pair of numbers. 22. 225 and 9 Solve for a and b. 23. 24. 25. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. 4 Name: ________________________ ID: A 26. Jason wants to walk the shortest distance to get from the parking lot to the beach. a. b. How far is the spot on the beach from the parking lot? How far will his place on the beach be from the refreshment stand? 27. Use the Side-Splitter Theorem to find x, given that PQ Ä BC . Solve for x. 28. 5 Name: ________________________ ID: A 29. → 30. LO bisects ∠NLM , LM = 18, NO = 4, and LN = 10. Find OM. 6 ID: A Chapter 7 review Answer Section MULTIPLE CHOICE 1. C 2. B 3. A SHORT ANSWER 4. 5. 6. 7. 8. 9. 10. 60 : 1 4b 9 –3 14.3 ft 13 in. by 9 in. x = 3; y = 12 11. ∆RST ∼ ∆UVW ; 5 6 12. x = 9, y = 27 13. AB = 10; EF = 2 14. 22.2 in. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 272.6 cm 2 yes, by AA ∆ABC ∼ ∆MNO ; SSS ∆ADB ∼ ∆CDB; SAS 2 AA Postulate; 6 3 3 AA Postulate; 17 5 20 ft 45 9 15 a = , b = 2 2 400 580 a = , b = 21 21 25. 133 26. 24 m; 32 m 27. 12 28. 5 1 ID: A 29. 52 3 30. 7.2 2

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