WARM-UP   x = 18 t = 3, -7 u = ±7

7-2 Similar Polygons I CAN Use the definition of similar polygons to determine if two polygons are similar Determine the similarity ratio between two polygons. Create a similar figure using a similarity ratio

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.

Review Congruent Triangles  Does AAA prove triangles are congruent? What would AAA prove? Two polygons are similar if and only if: 1. ALL corresponding angles are congruent 2. ALL corresponding sides are proportional.

} Is PQR similar to ZYX ? Y Q 9 15 10 6 P R X Z 18 12 Are corresponding angles equal? Are ratios of corresponding sides equal? < Q  < Y < P  < Z } Given PQ = 9 = 3 ZY 6 2 PR = 18 = 3 ZX 12 2 < R  < X 3rd Angle Theorem RQ = 15 = 3 YX 10 2 YES YES

A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

How is the similarity ratio and scale factor related? The similarity ratio is the reciprocal of the scale factor!

Similarity Statement PQR ZYX ~ “is similar to” Y Q 9 15 10 6 P R X Z 18 12 The similarity ratio of triangle PQR to triangle ZYX is 9 to 6 or 9 = 3 6 2 The similarity ratio of triangle ZYX to triangle PQR is 6 to 9 or 6 = 2 9 3

Example } Is ABC similar to KLJ ? J 10 K B 18 2 8 4 A C 5 L Are corresponding angles equal? Are ratios of corresponding sides equal? < A  < K < B  < L } Given AB = 2 = 1 KL 4 2 BC = 8 = 4 JL 18 9 < C  < J 3rd Angle Theorem YES NO, the sides are not proportional!

Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order. Writing Math

Application Problem Model = 1 = x Actual 400 1,000 You are building a model of the school. The similarity ratio of the model to the actual building is 1 400 If the actual building is 1,000 ft wide, how wide is the model? Model = Actual 1 = x 400 1,000 x = 2.5 feet wide

Your Turn The ratio of a model scale die cast motorcycle is 1:18. The model is 5 ¼ inches long. What is the length of the actual motorcycle in feet and inches? 7 ft 10 ½ in