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Chapter 9

Chapter 9. Proportions and Similarity. Using Ratios and Proportions. 9-1. Using Ratios and Proportions. 9-1. Objective: Use ratios and proportions to solve problems. EX Write each ratio in simplest form. EX Write each ratio in simplest form.

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Chapter 9

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  1. Chapter 9 Proportions and Similarity

  2. Using Ratios and Proportions 9-1

  3. Using Ratios and Proportions 9-1 Objective: Use ratios and proportions to solve problems EX Write each ratio in simplest form.

  4. EX Write each ratio in simplest form.

  5. Proportion – an equation that shows two equivalent ratios EX

  6. EX

  7. EX

  8. 9-2 Similar Polygons

  9. Objective: Identify similar polygons. 9-2 Similar Polygons Polygon – a closed figure in a plane formed by segments. Similar polygons – polygons that are the same shape but not necessarily the same size.

  10. Yes; the corresponding angles are congruent and the ratios are equal.

  11. No; the corresponding angles are not congruent.

  12. Because ABC ~ YXZ, you can write and solve a proportion. x 40 12 30 = EX If ABC ~ YXZ, find the value of x. 30x = 12  40 30x = 480 30 30 x = 16 8-2

  13. 4 4 -8 -8 4 4

  14. The actual dimensions of the living room are 24 feet by 20 feet.

  15. 9-3 Similar Triangles

  16. 9-3 Similar Triangles Objective: Use AA, SSS, and SAS similarity tests for triangles.

  17. GHK ~ JMP by SSS similarity.

  18. Find the value of x. QRN ~ XWT by SAS similarity. 3x = 45 x = 15

  19. 12 18 8x = 168 x = 21 The triangles are similar by SAS.

  20. x 4x = 108 x = 27 The tree is 27 ft tall.

  21. Proportional Parts and Triangles 9-4

  22. Proportional Parts and Triangles 9-4 Objective: Identify and use the relationships between proportional parts of triangles.

  23. H F G K F J 6x = 72 x = 12

  24. 4(x + 2) = 5x 4x + 8 = 5x -4x -4x 8 = x

  25. 9-5 Triangles and Parallel Lines

  26. Objective: Use proportions to determine whether lines are parallel to the sides of triangles. 9-5 Triangles and Parallel Lines

  27. 10 V

  28. 6a

  29. Proportional Parts and Parallel Lines Objective: Identify and use the relationships between parallel lines and proportional parts. 9-6

  30. RS

  31. 12x = 270 x = 22.5

  32. Perimeters and Similarity Objective: Identify and use proportional relationships of similar triangles. 9-7

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