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Name �——————Date 6.1For use with pages 372–379Simplify the ratio.1. 12 : 1632 in.22. }8 in.26 cm3. }14 cm10 in.4. }2 ft5. 3 gallons : 10 quarts6. 28 oz : 2 lbFind the ratio of the width to the length of the rectangle. Then simplifythe ratio.7.8.9.4 cm6 in.12 cm1 ft10 in.18 in.Use the number line to find the ratio of the distances.AB0123AB10. }CFC456BF11. }CDDE78DE12. }ACF9101112BE13. }AD14. Perimeter The perimeter of a rectangle is 56 inches. The ratio of the length to theCopyright Holt McDougal. All rights reserved.width is 6 : 1. Find the length and the width.15. Area The area of a rectangle is 525 square centimeters. The ratio of the length tothe width is 7 : 3. Find the length and the width.The measures of the angles of a triangle are in the extended ratio given.Find the measures of the angles of the triangle.16. 1 : 7 : 1017. 5 : 6 : 718. 7 : 14 : 15x419. } 5 }15520520. } 5 }y827z1221. } 5 }1241322. } 5 }x26x2323. } 5 }m11m155224. } 5 }3k 2 4k21Solve the proportion.GeometryChapter 6 Resource Book71

Name �——————LESSON6.1Date uedFor use with pages 372–379Find the geometric mean of the two numbers.25. 2 and 826. 3 and 927. 7 and 1428. 8 and 1629. 10 and 1230. 9 and 13Let x 5 6, y 5 3, and z 5 2. Write the ratio in simplest form.2x 1 y31. }34z 2 332. }xz 1 2y33. }2x 2 42y 2 3y2235. } 5 }52z12836. } 5 }4z22Solve the proportion.x1234. } 5 }4xIn Exercises 37–39, the ratio of two side lengths for the triangle is given.Solve for the variable.37. AC : AB is 3 : 4.38. AB : CB is 2 : 1.39. AC : BC is 7 : 4.CCA21C242x 1 4xAA1216xBBBof the length to the width is 5 : 3. Find the area of the lawn.In Exercises 41 and 42, use the following information.Golden Gate Bridge You purchase a scale model of the Golden Gate Bridge, which islocated near San Francisco, California. The model states that the scale is 1 inch : 50 feet.The actual length of the bridge is 8980 feet.41. What is the length of the model?42. The model is approximately 15 inches tall.What is the actual height of the bridge?72GeometryChapter 6 Resource BookCopyright Holt McDougal. All rights reserved.40. Area The perimeter of the rectangular front lawn of the library is 192 feet. The ratio

Name �——————LESSON6.2Date ————————————PracticeFor use with pages 380–386Copy and complete the statement.5?661. If } 5 }, then } 5 }.y?5x?yxx2. If } 5 }, then } 5 }.26?12y7?xx143. If } 5 }, then } 5 }.y44?x9?114. If } 5 }, then } 5 }.y22?Decide whether the statement is true or false.83xy5. If } 5 }, then } 5 }.38yxy83x6. If } 5 }, then } 5 }.38yx83xx7. If } 5 }, then } 5 }.3yy88yxx8. If } 5 }, then } 5 }.33y88y13x18x9. If } 5 }, then } 5 }.33y8814xx 1 2y10. If } 5 }, then } 5 }.33yyUse the diagram and the given information to find the unknown length.AEAB11. Given } 5 }, find BC.EDBCAEAB12. Given } 5 }, find BC.EDBCAA1261812EBEB433DCDCopyright Holt McDougal. All rights reserved.CCDFD13. Given } 5 }, find BE.BEFEFEAB14. Given } 5 }, find AC.EDBCFFA9EBC16B4E53DC6D15. Multiple Choice If m, n, p, and q are four different numbers, and the proportionpm} 5 } is true, which of the following is false?qnA. mq 5 pnB. m 5 p and n 5 qq1pn1mC. } 5 }pmGeometryChapter 6 Resource Book73

Name �——————LESSON6.2Date uedFor use with pages 380–38616. Error Analysis Describe and correct the error made in the reasoning.ab5bIf }5 5 }3, then }a 5 }3 . 17. Map Scale On a map, two neighboring towns are 2.4 inches apart. The actualstraight line distance between the two towns is 36 miles. What is the scale ofthe map?18. Collinear Points The points (23, 23), (21, 1), and (2, y) are collinear.1 2 (23)21 2 (23)y21Find the value of y by solving the proportion } 5 }.2 2 (21)19. Sales Tax You plan on purchasing a new 25,000 vehicle. Recently, a friend boughta 22,500 vehicle and paid an additional 1575 in sales tax. Assuming the samesales tax rate applies, how much should you expect to pay in sales tax?In Exercises 20 and 21, use the following information.Scale Model You purchase a scale model of a train.The model states that the scale is 1 inch : 5.4 feet.20. If the model is 10 inches long, how long is the actual train?21. The actual height of the train is 13.5 feet, how tall is the model?Mexican Pesos In November, 2005, the exchange rate of Mexican pesos toU.S. dollars was 10.77 to 1. While on vacation, you paid 205 pesos fora sombrero at a gift shop.22. What was the price of the sombrero in U.S. dollars?23. If the exchange rate were 9.24 Mexican pesos to 1 U.S. dollar, what would have beenthe cost in U.S. dollars?In Exercises 24 and 25, use the following information.Canadian Dollars In November, 2005, the exchange rate of Canadian dollars toU.S. dollars was 1 to 0.85. A Canadian citizen paid 12.28 in U.S. dollarsfor lunch while visiting New York City.24. What was the price of the lunch in Canadian dollars?25. If the exchange rate were 1.28 Canadian dollars to 1 U.S. dollar, what would havethe cost been in Canadian dollars?74GeometryChapter 6 Resource BookCopyright Holt McDougal. All rights reserved.In Exercises 22 and 23, use the following information.

Name �——————Date 6.3For use with pages 387–395List all pairs of congruent angles for the figures. Then write the ratios ofthe corresponding sides in a statement of proportionality.1. n ABC , nDFE2. WXYZ , MNOPADBWXZCYMNFEPO3. Multiple Choice Triangles ABC and DEF are similar. Which statement isnot correct?AB BCA. }5 }EFDEABCAB. } 5 }DEFDC. A FDetermine whether the polygons are similar. If they are, write a similaritystatement and find the scale factor.4.5.D24WXAD5656166446Copyright Holt McDougal. All rights reserved.CB3CE4A16BFZY24In the diagram, WXYZ , MNOP.6. Find the scale factor of WXYZ to MNOP.7. Find the values of x, y, and z.P108. Find the perimeter of WXYZ.W9. Find the perimeter of MNOP.y10. Find the ratio of the perimeter of MNOP tothe perimeter of WXYZ.12Z12z8YMX8Ox135810NGeometryChapter 6 Resource Book75

Name �——————Date continuedFor use with pages 387–3956.3The two triangles are similar. Find the values of the variables.11.12.156n5.5m108m12m 4In Exercises 13 and 14, use the following information.Similar Triangles Triangles RST and WXY are similar. The side lengths of nRST are10 inches, 14 inches, and 20 inches, and the length of an altitude is 6.5 inches. The shortestside of nWXY is 15 inches long.13. Find the lengths of the other two sides of nWXY.14. Find the length of the corresponding altitude in nWXY.15. Multiple Choice The ratio of one side of n ABC to the corresponding side of asimilar nDEF is 4 : 3. The perimeter of nDEF is 24 inches. What is the perimeterof n ABC?A. 18 inchesB. 24 inchesC. 32 inchesIn the diagram, nXYZ , nMNP.16. Find the scale factor of nXYZ to nMNP.X17. Find the unknown side lengths of both triangles.18. Find the length of the altitude shown in nXYZ.Z6YM19. Find and compare the areas of both triangles.105.89PIn Exercises 20–22, use the following information.Swimming Pool The community park has a rectangular swimming pool enclosed by arectangular fence for sunbathing. The shape of the pool is similar to the shape of the fence.The pool is 30 feet wide. The fence is 50 feet wide and 100 feet long.20. What is the scale factor of the pool to the fence?21. What is the length of the pool?22. Find the area reserved strictly for sunbathing.76GeometryChapter 6 Resource BookNCopyright Holt McDougal. All rights reserved.4

Name �——————FOCUS ON6.3Date ————————————PracticeFor use with pages 396–3971. Find the 16th, 17th, 18th, and 19th terms of the Fibonacci sequence.2. Find the 20th, 21st, 22nd, and 23rd terms of the Fibonacci sequence.3. Find the 24th, 25th, 26th, and 27th terms of the Fibonacci sequence.4. Find the 28th, 29th, 30th, and 31st terms of the Fibonacci sequence.5. Find the ratios of consecutive terms from Exercise 1.6. Find the ratios of consecutive terms from Exercise 2.7. Find the 1st, 2nd, 3rd, 4th, 5th, and 6th terms of a Fibonacci sequence starting withthe numbers 12 and 16.8. Find the ratios of consecutive terms from Exercise 7.9. Draw a golden rectangle in the space below. Measure the length and width of yourCopyright Holt McDougal. All rights reserved.rectangle and find their ratio. How does your answer compare to the golden ratio?10. Challenge The formula to find the nth term of the Fibonacci sequence is}}(1 1 Ï 5 )n 2 (1 2 Ï5 )nFib(n) 5 }}. Use this formula to find the 40th, 50th,}2n Ï 5and 60th term of the Fibonacci sequence.GeometryChapter 6 Resource Book77

Name �——————Date 6.4For use with pages 399–405Use the diagram to complete the statement.1. n ABC ,3. B CA?AB2. } 5 } 5 }EF?8?4. } 5 }?12?5. x 5A66. y 5xCB8D16?12yFEDetermine whether the triangles are similar. If they are, write asimilarity 58XL 858858KZ11.PJKNL508MY12. G508MTQ 458R858KNSH78GeometryChapter 6 Resource BookCopyright Holt McDougal. All rights reserved.B

Name �——————LESSON6.4Date uedFor use with pages 399–40513. Multiple Choice In the diagram at the right,}find the length of BC.AB428A. }5B. 6C. 320D. }7C75DEIn Exercises 14–17, use the diagram at the right.AB14. List three pairs of congruent angles.C15. Name two pairs of similar triangles and write asimilarity statement for each.D16. Is n ACD , nBCE?E17. Is nAED nEAB?In Exercises 18–21, use the diagram at the right.Find the coordinates of point Z so that nRST , nRXZ.yS18. R(0, 0), S(0, 4), T(28, 0), X(0, 2), Z(x, y)X19. R(0, 0), S(0, 6), T(26, 0), X(0, 2), Z(x, y)TZR20. R(0, 0), S(0, 10), T(220, 0), X(0, 6), Z(x, y)xCopyright Holt McDougal. All rights reserved.21. R(0, 0), S(0, 7), T(29, 0), X(0, 4), Z(x, y)22. Multiple Choice Triangles ABC and DEF are right triangles that are similar.}}}}AB and BC are the legs of the first triangle. DE and EF are the legs of the secondtriangle. Which of the following is false?A. A DB. AC 5 DFABACC. } 5 }DEDFIn Exercises 23–25, use the following information.Flag Pole In order to estimate the height h of a flagpole, a 5 foot tall male student stands so that the tipof his shadow coincides with the tip of the flag pole’sshadow. This scenario results in two similar trianglesas shown in the diagram.DhB23. Why are the two overlapping triangles similar?24. Using the similar triangles, write a proportionthat models the situation.AC6 ft5 ft12 ftE25. What is the height h (in feet) of the flag pole?Check that your answer is reasonable.GeometryChapter 6 Resource Book79

Name �——————Date 6.5For use with pages 406–413Is either nLMN or nRST similar to n TDetermine whether the two triangles are similar. If they are similar, writea similarity statement and find the scale factor of n A to nB.4.JL3 A858JX4K16858181012BZXAB9LKY16ZYNot drawn to scale5. Algebra Find the value of m that makes n ABC , nDEF when AB 5 3, BC 5 4,DE 5 2m, EF 5 m 1 5, and B E.Show that the triangles are similar and write a similarity statement.Explain your reasoning.6.PR8083.5T6Q27. G4K857H10GeometryChapter 6 Resource BookS4MNCopyright Holt McDougal. All rights reserved.3.