5.2 Similar Polygons

1. 5.2 Similar Polygons • Two congruent polygons are also similar polygons. • Two polygons are similar iff (if and only if) two conditions are satisfied. • All pairs of corresponding angles are congruent. • All pairs of corresponding sides are proportional. • The symbol ~ is used to symbolize similarity. • The symbol  is used to symbolize correspondence. Section 5.2 Nack

2. Similar Polygons. • The vertices of the congruent angles are corresponding vertices. • The sides opposite congruent angles are corresponding sides. For example, in this diagram, since A  H and B  J it follows that: vertices A  H and A  H B  J and B  J and the included sides: AB  HJ Section 5.2 Nack

3. Similar Triangles If ΔABC ~ ΔDEF, find the measures of the remaining parts of each triangle. • mA =180 – 90-37 = 53 • Similarity of corresponding vertices tells us that: mD = 53 mE = 90 mF = 37 • The proportion that relates the length of the sides is: AB = BC = AC DE EF DF 3 = 4 = 5 • EF DF Solving each proportion: EF = 8 and DF = 10 4 3 37 5 6 Section 5.2 Nack