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Exploring Similar Figures with Ratios Lesson

Learn to determine similarity of figures with ratios. Understand corresponding sides and angles. Practice with examples to improve understanding.

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Exploring Similar Figures with Ratios Lesson

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 138 = 144; not equal Warm Up Find the cross products, and then tell whether the ratios are equal. 16 6 40 15 , 1. 240 = 240; equal 3 8 18 46 , 2. 8 9 24 27 , 3. 216 = 216; equal 28 12 42 18 , 4. 504 = 504; equal

  3. Problem of the Day Every 8th telephone pole along a road has a red band painted on it. Every 14th pole has an emergency call phone on it. What is the number of the first pole with both a red band and a call phone? 56

  4. Learn to use ratios to determine if two figures are similar.

  5. Vocabulary similar corresponding sides corresponding angles

  6. Similarfigures are figures that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.”

  7. E B D F A C Corresponding angles of two or more similar polygons are in the same relative position. Corresponding sides of two or more similar polygons are in the same relative position. When naming similar figures, list the corresponding angles in the same order. For the triangles below, ∆ABC ~ ∆DEF.

  8. SIMILAR FIGURES Two figures are similar if • The measures of their corresponding angles are equal. • The ratios of the lengths of the corresponding sides are proportional.

  9. Reading Math A side of a figure can be named by its endpoints, with a bar above such as; AB Without the bar, the letters indicate the length of the side.

  10. AB corresponds to DE. BC corresponds to EF. AC corresponds to DF. ? ? = = ? ? = = ? ? = = Additional Example 1: Determining Whether Two Triangles Are Similar Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E 16 in 10 in A C 28 in D 4 in 7 in 40 in F B AB DE BC EF AC DF Write ratios using the corresponding sides. 4 16 10 40 7 28 Substitute the length of the sides. 1 4 1 4 1 4 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

  11. AB corresponds to DE. BC corresponds to EF. AC corresponds to DF. ? ? = = ? ? = = ? ? = = Check It Out: Example 1 Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E 9 in 9 in A C 21 in D 3 in 7 in 27 in F B AB DE BC EF AC DF Write ratios using the corresponding sides. 3 9 9 27 7 21 Substitute the length of the sides. 1 3 1 3 1 3 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

  12. Additional Example 2: Determining Whether Two Four-Sided Figures are Similar Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

  13. MN corresponds to QR. NO corresponds to RS. OP corresponds to ST. MP corresponds to QT. Additional Example 2 Continued MN QR NO RS OP ST MP QT

  14. ? ? ? OP ST MN QR NO RS MP QT = = = 8 12 6 9 4 6 10 15 ? ? ? = = = ? 2 3 2 3 2 3 2 3 ? ? = = = Additional Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

  15. M P 100 m 80° 65° 60 m 47.5 m 125° 90° O 80 m N Q T 400 m 80° 65° 240 m 190 m 125° 90° S R 320 m Check It Out: Example 2 Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

  16. M P 100 m MN corresponds to QR. 80° 65° 60 m 47.5 m 125° 90° O NO corresponds to RS. 80 m N Q T 400 m 80° 65° OP corresponds to ST. 240 m 190 m 125° MP corresponds to QT. 90° S R 320 m Check It Out: Example 2 Continued MN QR NO RS OP ST MP QT

  17. M P 100 m ? ? ? OP ST MN QR NO RS MP QT = = = 80° 65° 60 m 47.5 m 125° 90° O 80 m N 80 320 60 240 47.5 190 100 400 ? ? ? = = = Q T 400 m 80° 65° ? ? ? 1 4 1 4 1 4 1 4 = = = 240 m 190 m 125° 90° S R 320 m Check It Out: Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. 59° 59° 35° 86° 86° 35° Lesson Quiz: Part I Tell whether the figures are similar. 1. similar

  20. 119° 107° 55° 79° 135° 107° 38° 80° Lesson Quiz: Part II Tell whether the figures are similar. 2. not similar

  21. Lesson Quiz for Student Response Systems 1. Which of the following triangles are similar? A. C. B.D.

  22. Lesson Quiz for Student Response Systems 2. Which of the following figures are similar? A. B.

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