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Exercise

C. 5. 4. A. B. Z. 6. 10. 8. Y. X. 12. Exercise. ∆XYZ ~ ∆LMN. Dimensions are in inches. Find LM. 6 in. M. Y. P. 12. 16. L. N. 9.6. 10. W. X. Z. 20. Exercise. ∆XYZ ~ ∆LMN. Dimensions are in inches. Find MP. 4.8 in. M. Y. P. 12. 16. L. N. 9.6. 10. W. X. Z.

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Exercise

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  1. C 5 4 A B Z 6 10 8 Y X 12

  2. Exercise ∆XYZ ~ ∆LMN. Dimensions are in inches. Find LM. 6 in. M Y P 12 16 L N 9.6 10 W X Z 20

  3. Exercise ∆XYZ ~ ∆LMN. Dimensions are in inches. Find MP. 4.8 in. M Y P 12 16 L N 9.6 10 W X Z 20

  4. M Y L N 10 12 16 X Z 20 Exercise What is the ratio of the perimeter of ∆XYZ to the perimeter of ∆LMN? 2 : 1 9.6

  5. M Y L N 10 12 16 X Z 20 Exercise Find the area of of ∆LMN. 24 in.2 9.6

  6. M Y L N 10 12 16 X Z 20 Exercise What is the ratio of the area of ∆XYZ to the area of ∆LMN? 4 : 1 9.6

  7. Ratio of the Perimeters of Similar Polygons The ratio of the perimeters is equal to the ratio of the corresponding sides.

  8. 1612 43 = Example 1 The corresponding sides of two similar triangles are 16 in. and 12 in. The perimeter of the first triangle is 55 in. Find the perimeter of the second triangle, p2.

  9. 43 55p2 = 1612 43 4 4 = 4p2 = 3(55) 4p2 = 165 p2 = 41.25 in.

  10. 2s 20180 = Example 2 The perimeters of two similar hexagons are 20 ft. and 180 ft. The smaller hexagon has one side of 2 ft. Find the corresponding side of the larger hexagon.

  11. 2s 19 = 2s 20180 = s = 2(9) s= 18 ft.

  12. Example For the figure, write the missing factor: EF = __BC. D A E F B C 4 12 3

  13. 4 6 4a 6a

  14. Ratio of the Areas of Similar Polygons The ratio of the areas of similar polygons is equal to the ratio of the squares of the corresponding sides.

  15. 43 43 43 169 Example 3 The first of two regular pentagons has a side of 4 cm, and the second has a side of 3 cm. What is the ratio of their areas? 2 ( ) = × =

  16. 2 10A2 35 ( ) = Example 4 The first of two similar polygons has a side of 3 cm and an area of 10 cm2. The corresponding side of the second is 5 cm. What is the area of the second polygon?

  17. 10A2 925 = 9 9 9A2 = 10(25) 9A2 = 250 A2 ≈ 27.8 cm2

  18. 2 400100 s9 ( ) = Example 5 The areas of two similar pentagons are 400 mm2 and 100 mm2. One side of the smaller pentagon is 9 mm. Find the length of the similar side of the larger pentagon.

  19. 41 s281 = s = 324 s2 = 4(81) s2 = 324 s= 18 mm

  20. Example ∆ABC ~ ∆DEF. For the figure, write the missing factor: area of ∆DEF = __ area of ∆ABC. D A B C E F 4 12 9

  21. Example ∆ABC ~ ∆DEF. If the area of ∆ABC is 8 units2, what is the area of ∆DEF? D A B C E F 4 12 72 units2

  22. Example ∆ABC ~ ∆DEF. If the perimeter of ∆ABC is 14 units, what is the perimeter of ∆DEF? D A B C E F 4 12 42 units

  23. 12 12 Example There are 640 acres in a square mile. How many acres are in a parcel of land that is mi. × mi.? 160 acres

  24. Example How many square inches are in a rectangle that is 2 ft. × 3 ft.? 864 in.2

  25. Example How many square feet are in 288 in.2? 2 ft.2

  26. Example How many square feet are in a square yard? How many square inches are in a square yard? 9 ft.2; 1,296 in.2

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