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7-1 Ratios in Similar Polygons Warm Up 1. If ∆QRS ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. Holt McDougal Geometry 3. 7-1 Ratios in Similar Polygons Objectives Identify similar polygons. Apply properties of similar polygons to solve problems. Holt McDougal Geometry 7-1 Ratios in Similar Polygons Figures that are similar (~) have the same shape but not necessarily the same size. Holt McDougal 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 McDougal Geometry 7-1 Ratios in Similar Polygons Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. Holt McDougal Geometry 0.5 7-1 Ratios in Similar Polygons 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. Holt McDougal 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. Also, when writing the proportion statements for a given problem, make sure to always choose image to pre-image! You need to make sure to keep the proportions consistent. When you work with proportions, be sure the ratios compare corresponding measures. Holt McDougal Geometry 7-1 Ratios in Similar Polygons Example 2A: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH Holt McDougal Geometry 7-1 Ratios in Similar Polygons Example 2B: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆ABCD and ∆EFGH Holt McDougal Geometry 7-1 Ratios in Similar Polygons Example 3: Hobby Application Find the length of the model to the nearest tenth of a centimeter. Holt McDougal Geometry 7-1 Ratios in Similar Polygons Lesson Wrap up Copy and complete the graphic organizer. Write the definition of similar polygons, and a similarity statement. Then draw examples and non-examples of similar polygons. Holt McDougal Geometry