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

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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. x  5 9x = (36.35) (1.25)

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