8-2 Similar Polygons Objective: To identify and apply similar polygons 4/4/17 8-2 Similar Polygons Objective: To identify and apply similar polygons SIMILAR: Corresponding angles are congruent Corresponding sides are proportional SIMILAR RATIO: the ratio of the lengths of corresponding sides

Corr. sides are proportional m B = GH = FG CD x Ex: ABCD EFGH B C m E = ? F G m E = m A = 53 53o 127o Corr. s congruent A D E H AB = AD EF ? EF EH Corr. sides are proportional m B = GH = FG CD x 127° x = BC

ABC FED with a similarity ratio of ¾ or 3:4 Match up the biggest side of one Δ to the biggest side of the other, then the next biggest sides, and finally the smallest sides. Ex: If similar, write a similarity statement and give the similarity ratios. AC = 18 = 3 B E FD 24 4 15 12 16 20 AB = 15 = 3 A 18 C D F FE 20 4 24 BC = 12 = 3 ED 16 4 ABC FED with a similarity ratio of ¾ or 3:4

LM = ON Corr. Sides of cong. L 5 M Q 6 R QR TS polygons are prop. Isosceles Trapezoids Ex: LMNO QRST O 2 N T x S Find the value of x 3.2 LM = ON Corr. Sides of cong. L 5 M Q 6 R QR TS polygons are prop. 5 = 2 Substitution 6 x 5x = 12 Cross product property x = 2.4 Find SR to nearest tenth 5 = 3.2 6 y y = 3.84  3.8

GOLDEN RATIO: in any golden rectangle, the length : width 1.618:1 GOLDEN RECTANGLE: a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle GOLDEN RATIO: in any golden rectangle, the length : width 1.618:1 a + b = a a b

Assignment: Page 426 #13 – 17, 21 – 28