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Identify similar polygons. Apply properties of similar polygons to solve problems.

Learn to identify, describe, and apply properties of similar polygons. Understand similarity ratio, corresponding sides, and angles. Practice solving problems with examples.

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Identify similar polygons. Apply properties of similar polygons to solve problems.

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  1. 2-1: Properties of Similar Polygons Identify similar polygons. Apply properties of similar polygons to solve problems. Vocabulary similar similar polygons similarity ratio

  2. Figures that are similar(~) have the same shape but not necessarily the same size.

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

  4. Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. 0.5 N  Q and P  R, therefore M  T.

  5. Example 2 Identify the pairs of congruent angles and corresponding sides. B  G and C  H, By the Third Angles Theorem, A  J.

  6. A similarity ratiois 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.

  7. Example 3: 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.

  8. Example 3 Continued 5(6.3) = x(1.8) Cross Products Prop. 31.5 = 1.8x Simplify. 17.5 = x Divide both sides by 1.8. The length of the model is 17.5 centimeters.

  9. Example 4 4. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is . If the length of the model is 10 inches, what is the length of the actual sailboat in feet?

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