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NAME ____________________________________________ DATE _____________________________ PERIOD _____________ Notes and Practice Similar Polygons Identify Similar Polygons Similar polygons have the same shape but not necessarily the same size. Example 1: If △ABC ∼ △XYZ, list all pairs of congruent angles and write a proportion that relates the corresponding sides. Use the similarity statement. Congruent angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z !" !" !" Proportion: = = !" !" !" Example 2: Determine whether the pair of figures is similar. If so, write the similarity statement and scale factor. Explain your reasoning. Step 1 Compare corresponding angles. ∠W ≅ ∠P, ∠X ≅ ∠Q, ∠Y ≅ ∠R, ∠Z ≅ ∠S Corresponding angles are congruent. Step 2 Compare corresponding sides. !" !" !" !" = !" ! ! !" = , ! !" ! ! ! ! = !" !" ! !" = , ! !" = !" !" ! = , and ! = = . Since corresponding sides are proportional, ! WXYZ ∼ PQRS. The polygons are similar with a scale factor of . ! Exercises List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons. 1. △DEF ∼ △GHJ 2. PQRS ∼ TUWX Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. 3. Chapter 7 4. 12 Glencoe Geometry NAME ____________________________________________ DATE _____________________________ PERIOD _____________ 7-2 Study Guide and Intervention (continued) Similar Polygons Use Similar Figures You can use scale factors and proportions to find missing side lengths in similar polygons. Example 1: The two polygons are similar. Find x and y. Example 2: If △DEF ∼ △GHJ, find the scale factor of △DEF to △GHJ and the perimeter of each triangle. The scale factor is !" !" = ! ! !" = . ! The perimeter of △DEF is 10 + 8 + 12 or 30. Use the congruent angles to write the corresponding vertices in order. ! △RST ∼ △MNP ! ! Write proportions to find x and y. !" !" = ! !" !" ! = ! !" 32y = 38(16) x = 26 y = 19 = !"#$%"&"# !" △!"# !"#$%"&"# !" △!"# !" ! (3)(30) = 2x !" 16x = 32(13) = 45 = x Theorem 7.1 Substitution Cross Products Property Solve. So, the perimeter of △GHJ is 45. Exercises Each pair of polygons is similar. Find the value of x. 1. 2. 3. 4. 5. If ABCD ∼ PQRS, find the scale factor of ABCD to PQRS and the perimeter of each polygon. Chapter 7 13 Glencoe Geometry