169_186_CC_A_RSPC1_C12_662330.indd



7-2 Study Guide and InterventionSimilar PolygonsIdentify Similar Polygons Similar polygons have the same shape but not necessarily the same size.4327487157741Example 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 ? ∠ZProportion: ABXY = BCYZ = CAZXExample 2: Determine whether the pair of figures is similar. If so, write the similarity statement and scale factor. Explain your reasoning.362824143516Step 1 Compare corresponding angles.∠W ? ∠P, ∠X ? ∠Q, ∠Y ? ∠R, ∠Z ? ∠SCorresponding angles are congruent.Step 2 Compare corresponding sides.WXPQ = 128 = 32, XYQR = 1812 = 32, YZRS = 1510 = 32, andZWSP = 96 = 32. Since corresponding sides are proportional,WXYZ ～ PQRS. The polygons are similar with a scale factor of 32.Exercises3864909140447List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons.1. △DEF ～ △GHJ31999141696942. PQRS ～ TUWXDetermine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.3422650787402222501295403. 4. 7-2 Study Guide and Intervention (continued)Similar PolygonsUse 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.28261268543Use the congruent angles to write the corresponding vertices in order.△RST ～ △MNPWrite proportions to find x and y.3216 = x1338y = 321616x = 32(13) 32y = 38(16)x = 26 y = 191591012394410Example 2: If △DEF ～ △GHJ, find the scale factor of △DEF to △GHJ and the perimeter of each triangle.The scale factor is EFHJ = 812 = 23.The perimeter of △DEF is 10 + 8 + 12 or 30.23 = Perimeter of △DEF Perimeter of △GHJ Theorem 7.123 = 30xSubstitution(3)(30) = 2x Cross Products Property45 = x Solve.So, the perimeter of △GHJ is 45.ExercisesEach pair of polygons is similar. Find the value of x.368300603253370057603631. 2. 348615010160215900609603. 4. 34023301485905. If ABCD ～ PQRS, find the scale factor of ABCD to PQRS and the perimeter of each polygon. ................
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