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Objectives

Objectives. To set up ratios and solve proportions To identify similar polygons using ratios. Ratios. A ratio compares two numbers by division The ratios of 1 to 2, 1:2, and ½ all represent the same comparison Example:

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Objectives

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  1. Objectives • To set up ratios and solve proportions • To identify similar polygons using ratios

  2. Ratios • A ratio compares two numbers by division • The ratios of 1 to 2, 1:2, and ½ all represent the same comparison Example: The ratio of the side lengths of a quadrilateral are 2:3:5:6 and its perimeter is 80. What is the length of the shortest side? Let the lengths of the sides be 2x, 3x, 5x, and 6x. 2x + 3x + 5x + 6x = 80 (Definition of perimeter) 16x = 80 (Addition property) x = 5 (Division property) The short side is 2x = 10

  3. Proportions • A proportion is an equation stating that two ratios are equal • A proportion can be solved by cross-multiplying 15x = 5 * 12 = 60 x = 4

  4. Similarity Definition • Two figures that have the same shape are similar (~) • Two polygons are similar if and only if • their corresponding angles are congruent AND • their corresponding sides are proportional

  5. Nonexamples for Similarity • If two objects have congruent angles but not proportional corresponding sides, are they similar? • If two objects have proportional corresponding sides but not congruent angles, are they similar?

  6. Similarity Example 1 • Determine whether the two figures are similar. • If they are similar, write a similarity statement. B  G and C  H. By complementary angles, A  J. Since all corresponding angles are congruent and all corresponding sides are proportional, ΔBCA ~ ΔGHJ

  7. Similarity Example 2 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch. 9x = (36.35) (1.25) x  5

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