5-9 Similar Figures. The figures are similar. Find each missing measure. 1. ANSWER: ANSWER: 21 in.
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1 The figures are similar. Find each missing measure. 1. The figures are similar. Find each missing measure. 4. cm in km 21 in The logo for an electronics store is made from similar trapezoids as shown. What is the length of the missing measure? 9 ft 7. 2 units cm esolutions Manual - Powered by Cognero Page 1
2 8. The design shown is made using similar triangles and quadrilaterals. triangle A ~ triangle B and quadrilateral C ~ quadrilateral D. 11. Using a scale factor of, draw and label a rectangle similar to rectangle ABCD. a. Find the missing measure in triangle B. b. Find the missing measure in quadrilateral C. a. 10 in. b. 2.5 in. 9. Triangle LMN is similar to RST. What is the value of LT if RT is 9 inches, MN is 21 inches, and ST is 7 inches? 27 in. 10. Quadrilateral ABCD is similar to quadrilateral WXYZ. What is the value of WZ if AD is 18 feet, CD is 27 feet, and YZ is 10.8 feet? 7.2 ft 12. Using a scale factor of, draw and label a triangle similar to XYZ. esolutions Manual - Powered by Cognero Page 2
3 13. Figure FGHJK ~ figure LMNPQ. The scale factor from figure FGHJK to figure LMNPQ is. What is the perimeter of figure LMNPQ? 15. Multiple Representations In this problem, you will investigate the relationship between the perimeters of similar figures. In the figures below, ABC ~ XYZ. 102 m 14. An image that is projected onto a movie screen measures 8.8 meters by 6.4 meters. The projection is similar to the individual frame on the movie reel. If the projection has a scale factor of 400, what are the original dimensions of a frame on a movie reel? 22 mm by 16 mm a. Geometry Write an expression for the perimeter of ABC. b. Symbols If the scale factor is represented by d, write algebraic expressions for the measures of the sides of XYZ. c. Geometry Write an expression for the perimeter of XYZ. d. Symbols Use the Distributive Property to factor the expression from part c. Explain the meaning of the expression. e. Make A Prediction Suppose AB = 3 inches, BC = 4 inches, AC = 5 inches, and the scale factor from ABC to XYZ is 2. Find the perimeter of XYZ without calculating the lengths of,, and. Justify your procedure. f. Words Explain how the perimeters of similar figures are related to the scale factor. a. a + b + c b. ad, bd, cd c. ad + bd + cd d. d(a + b + c); Sample answer: The scale factor times the sum of the measures of the sides of ABC will give the perimeter of XYZ. e. 3 in. + 4 in. + 5 in. = 12 in.; 12 2 = 24; The perimeter of XYZ is 24 inches. f. Sample answer: If the figures are similar, then the perimeters are also similar. So, the perimeters are proportional. esolutions Manual - Powered by Cognero Page 3
4 16. Justify Conclusions Draw two similar triangles whose scale factor is 1: 3. Justify your answer. Sample answer: 20. Persevere with Problems True or false? If XYZ ~ RST, then, where x is the side opposite X, z is the side opposite Z, and so on. Justify your answer. If false, provide a counterexample. They are proportional; Sample answer: If XYZ ~ RST, then corresponding sides are proportional, so. Reason Inductively Determine whether each statement is always, sometimes, or never true. Explain your reasoning. 17. All rectangles are similar. Sometimes; sample answer: Even though all rectangles have congruent corresponding angles, the sides of one rectangle are not always proportional to the sides of another rectangle. 18. All squares are similar. Always; sample answer; All squares are similar because all four sides are of equal length. 19. Find the Error Tony is finding the length of where ABC ~ DEF, BC = 16 feet, EF = 12 feet, and DE = 18 feet. Find his mistake and correct it. 21. Building on the Essential Question Suppose you have two triangles. Triangle A is similar to triangle B, and the measures of the sides of triangle A are less than the measures of the sides of triangle B. The scale factor is Which is the original triangle? Explain. Triangle B is the original triangle. Since the scale factor is less than 1, the original triangle is being reduced, which means that the scaled triangle will be smaller. The measures of the sides of triangle A are less than the measures of the sides of triangle B, so triangle B must be the original triangle. 22. Quadrilateral ABCD is similar to quadrilateral EFGH. What is the length of? Tony wrote the proportion incorrectly. He should have solved the problem like this: A 1.5 m B 3.8 m C 4 m D 5.3 m C esolutions Manual - Powered by Cognero Page 4
5 23. If polygon ABCDE is similar to polygon FGHIJ, which of the following is not true? F ABC FGH G EDC JIH H J J corresponds to corresponds to 24. Triangle RST is similar to triangle XYZ. 26. The Statue of Zeus at Olympia is one of the Seven Wonders of the World. On a scale model of the statue, the height of Zeus is 8 inches. a. If the actual height of Zeus is 40 feet, what is the scale? b. What is the scale factor? a. 1 in. = 5ft b. 27. Flor is making bracelets. She knows that 4 bags of beads will make 14 bracelets. If she wants to make 56 bracelets, how many bags of beads will she need? 16 bags What is the length of? A in. B 3.75 in. C 4.8 in. D 9.6 in. 28. A bushel of apples will make approximately 3 gallons of apple cider. The table shows the relationship between the number of bushels of apples and the number of gallons of apple cider. C 25. Short Response Triangle LMN has a perimeter of 24 centimeters and is similar to triangle DEF. If the scale factor relating LMN to DEF is, what is the perimeter of 72 DEF? a. Given b, the number of bushels needed, write an equation that can be used to find g, the number of gallons of apple cider. b. How many bushels are needed to make 54 gallons of cider? a. g = 3b b. 18 bushels Multiply esolutions Manual - Powered by Cognero Page 5
6 30. Find each quotient. Express using exponents. or or Divide x k esolutions Manual - Powered by Cognero Page 6
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