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ABC ~ XYZ

BC YZ. ? XZ. =. a.  B  Y and m  Y = 78, so m  B = 78 because congruent angles have the same measure. AC XZ. BC YZ. b. Because AC corresponds to XZ ,. =. Similar Polygons. LESSON 7-2. Additional Examples. ABC ~ XYZ. Complete each statement. a. m  B = ? b.

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ABC ~ XYZ

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  1. BC YZ ? XZ = a.BY and mY = 78, so mB = 78 because congruent angles have the same measure. AC XZ BC YZ b.Because AC corresponds to XZ, . = Similar Polygons LESSON 7-2 Additional Examples ABC ~ XYZ Complete each statement. a.mB = ? b. Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. Quick Check

  2. Check that the corresponding sides are proportional. 1 2 AB JK 2 4 BC KL 1 2 CD LM 2 4 DA MJ = = = = Similar Polygons LESSON 7-2 Additional Examples Determine whether the parallelograms are similar. Explain. Corresponding sides of the two parallelograms are proportional. Check that corresponding angles are congruent. B corresponds to K, but mB≠mK, so corresponding angles are not congruent. Although corresponding sides are proportional, the parallelograms are not similar because the corresponding angles are not congruent. Quick Check

  3. Because ABC ~ YXZ, you can write and solve a proportion. AC YZ BC XZ = Corresponding sides are proportional. x 40 12 30 = Substitute. 12 30 Solve for x. x =  40 Similar Polygons LESSON 7-2 Additional Examples If ABC ~ YXZ, find the value of x. x = 16 Quick Check

  4. postcard width postcard length painting width painting length Corresponding sides are proportional. = x 24 6 36 = Substitute. 6 36 Solve for x. x =  24 Similar Polygons LESSON 7-2 Additional Examples A painting is 24 in. wide by 36 in. long. The length of a postcard reduction of the painting is 6 in. How wide is the postcard? The postcard and the painting are similar rectangles, so you can write a proportion. Let x represent the width of the postcard. x = 4 The postcard is 4 in. wide. Quick Check

  5. Let represent the longer side of the tabletop. 40 1.618 1 Write a proportion using the golden ratio. = = 64.72 Cross-Product Property Similar Polygons LESSON 7-2 Additional Examples The dimensions of a rectangular tabletop are in the golden ratio. The shorter side is 40 in. Find the longer side. The table is about 65 in. long. Quick Check

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