7 1 Ratios in Similar Polygons Objectives Identify

7 -1 Ratios in Similar Polygons Objectives Identify similar polygons. Apply properties of similar polygons to solve problems. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons _______(~) – figures that have the same shape but not necessarily the same size. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 1 A: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. Holt Mc. Dougal Geometry 0. 5

7 -1 Ratios in Similar Polygons Check It Out! Example 1 B Identify the pairs of congruent angles and corresponding sides. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons ________– 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. Holt Mc. Dougal Geometry .

7 -1 Ratios in Similar Polygons Writing Math Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 2 A: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 2 A Continued Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding sides. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 2 B: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆PQR and ∆STW Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 2 B Continued Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding angles. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Check It Out! Example 2 C Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding sides. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Helpful Hint When you work with proportions, be sure the ratios compare corresponding measures. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Example 3 A: Hobby Application Find the length of the model to the nearest tenth of a centimeter. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Check It Out! Example 3 B 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. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Check It Out! Example 3 B Continued 1. 25(36. 25) = x(9) 45. 3 = 9 x 5 x Cross Products Prop. Simplify. Divide both sides by 9. The length of the model is approximately 5 inches. Holt Mc. Dougal Geometry

7 -1 Ratios in Similar Polygons Warm Up Turn in for a grade. Please use complete sentences with proper grammar. Explain what a scale on a map means, how it is used, and how it is related to the concept of a similarity ratio. Holt Mc. Dougal Geometry