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LESSON 8.2: SIMILAR POLYGONS OBJECTIVES: To identify similar polygons To apply similar polygons Mrs. McConaughy Geometry 1 Similar Figures have the same shape, Similar figures ________________ but not necessarily the same size. ___________________________, Mrs. McConaughy Geometry 2 Similar Polygons Two polygons are similar if and only if ALL their NOTE: corresponding angles are Both conditions congruent must be met for two polygons to be determined AND to be similar. ALL their corresponding sides are proportional (equal ratios). The mathematical symbol for similarity is is similar to ________ and is read “___________.” : Mrs. McConaughy Geometry 3 UNDERSTANDING SIMILARITY Given: V ABC : V XYZ “is similar to” V XYZ Read: V ABC ______________ ALL corresponding angles A _____ X _____ B _____ Y _____ C _____ Z _____ ALL corresponding sides proportional BC = ___ ___ AB = ___ AC XY YZ Mrs. McConaughy Geometry XZ 4 DETERMINING SIMILARITY Is ABCD similar to JKLM? Recall: BOTH conditions must be met for two polygons to be determined to be similar. Recall: Consecutive angles of a Opposite angles of a supplementary are _________________. congruent are _____________________. Mrs. McConaughy Geometry 5 USING SIMILAR FIGURES Given: V ABC : V YXZ. Find the value of x. Mrs. McConaughy Geometry 6 Sketch ∆ XYZ and ∆ MNP with X M , Y N, Z P. Recall: BOTH conditions Label XY = 12, YZbe= met 14, ZX = 16, MN = 18, must for two polygons NP = 21, and PM = to 24.be determined to be similar. Determine whether the two triangles are similar. Mrs. McConaughy Geometry 7 The Golden Ratio A golden rectangle is a__________________________ rectangle that can be divided __________________________ into a square and a rectangle that is similar to the original ___________________________ __________________________. rectangle. The golden ratio is __________________________ the ratio, length: width, in a __________________________. golden rectangle, 1.618: 1 Mrs. McConaughy Geometry 8 USING THE GOLDEN RATIO KEY: Length = 1.618 Width 1 The dimensions of a rectangular tabletop are in the Golden Ratio. The shorter side is 40 inches. Find the longer side. Use a calculator. Mrs. McConaughy Geometry 9 FINAL CHECKS FOR UNDERSTANDING 1. If two polygons are similar, must they also be congruent? Explain. 2. Find the values of a and b, given that the two polygons are similar. 3. Now, list ALL pairs of congruent angles and ALL pairs of proportional sides. Mrs. McConaughy Geometry 10 Homework: Mrs. McConaughy Geometry 11