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Ratios in Similar Polygons Figures that are similar (~) have the same shape but not necessarily the same size. Holt McDougal Geometry 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 Ratios in Similar Polygons Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. Holt McDougal Geometry 0.5 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 __2:1_____. The similarity ratio of ∆DEF to ∆ABC is __1:2_____. Holt McDougal Geometry 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 McDougal Geometry Ratios in Similar Polygons Example 2A: Identifying Similar Polygons Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. Holt McDougal Geometry Ratios in Similar Polygons Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding sides. Thus the similarity ratio is Holt McDougal Geometry , and rect. ABCD ~ rect. EFGH. 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 Ratios in Similar Polygons Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding angles. Holt McDougal Geometry Ratios in Similar Polygons Example 3: Hobby Application Find the length of the model to the nearest tenth of a centimeter. Holt McDougal Geometry Ratios in Similar Polygons Lesson Quiz: Part I 1. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. no 2. 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? 25 ft Holt McDougal Geometry Ratios in Similar Polygons Lesson Quiz: Part II 3. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar. Always Holt McDougal Geometry Ratios in Similar Polygons Homework: Page 249 – 250 #’s 1 – 20 all #’s 27 – 29 all Holt McDougal Geometry