Mrs. McConaughy Geometry1 LESSON 8.2: SIMILAR POLYGONS OBJECTIVES:  To identify similar polygons  To apply similar polygons

Mrs. McConaughy Geometry2 Similar Figures Similar figures ________________ ___________________________, have the same shape, but not necessarily the same size.

Mrs. McConaughy Geometry3 Similar Polygons Two polygons are similar if and only if  ALL their corresponding angles are congruent AND  ALL their corresponding sides are proportional (equal ratios). The mathematical symbol for similarity is ________ and is read “___________.” is similar to NOTE: Both conditions must be met for two polygons to be determined to be similar.

Mrs. McConaughy Geometry4 UNDERSTANDING SIMILARITY Given: Read: “is similar to” ALL corresponding angles ALL corresponding sides proportional ___ = ___ = ___ XA YB Z C AB XY BC YZ AC XZ

Mrs. McConaughy Geometry5 DETERMINING SIMILARITY Is ABCD similar to JKLM? Recall: Consecutive angles of a are _________________. Opposite angles of a are _____________________. supplementary congruent Recall: BOTH conditions must be met for two polygons to be determined to be similar.

Mrs. McConaughy Geometry6 USING SIMILAR FIGURES Given:

Mrs. McConaughy Geometry7 Sketch ∆ XYZ and ∆ MNP with Recall: BOTH conditions must be met for two polygons to be determined to be similar.

Mrs. McConaughy Geometry8 The Golden Ratio A golden rectangle is __________________________ __________________________ ___________________________ __________________________. The golden ratio is __________________________ __________________________. a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle. the ratio, length: width, in a golden rectangle, 1.618: 1

Mrs. McConaughy Geometry9 USING THE GOLDEN RATIO The dimensions of a rectangular tabletop are in the Golden Ratio. The shorter side is 40 inches. Find the longer side. Use a calculator. KEY: Length = Width 1

Mrs. McConaughy Geometry10 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. FINAL CHECKS FOR UNDERSTANDING

Mrs. McConaughy Geometry11 Homework: