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Ratios in Similar Polygons

Ratios in Similar Polygons. Students will be able to apply properties of similar polygons to solve problems. Similarity. Figures that are similar ( ∼ ) have the same shape but not necessarily the same size .

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Ratios in Similar Polygons

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  1. Ratios in Similar Polygons Students will be able to apply properties of similar polygons to solve problems

  2. Similarity • Figures that are similar (∼) have the same shape but not necessarily the same size. • Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. • A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. Unit F

  3. Similar Figures • When we write a similarity statement, ΔABC ∼ΔLMN for two triangles, we always write each corresponding part in the same order. For example: If, then ∠A corresponds to ∠L, ∠B corresponds to ∠M, and ∠C corresponds to ∠N. Also, corresponds to ___ corresponds to ___ and corresponds to ___. B M N L A C Unit F

  4. Example 1: Determining Similarity Determine if ∆MLJ ~ ∆NPS. If so, write the similarity ratio and a similarity statement. Step 1: Identify pairs of congruent angles. M  N, L  P, J  S Step 2: Compare corresponding sides. Unit F

  5. Example 2: Hobby Application • Find the length of the model to the nearest tenth of a centimeter. • Let x be the length of the model in centimeters. • The rectangular model of the racing car is similar to the rectangular racing car, so the corresponding lengths are proportional. Unit F

  6. Example 2 (Continued) 5(6.3) = x(1.8) 31.5 = 1.8x 17.5 = x The length of the model is. Unit F

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