8 Date: Topic: Similar Triangles __ (7.5) Warm-up: 6 The shapes are similar. Find the similarity ratio, x, and y y 93° x x Similarity ratio = = Similar shapes have congruent corresponding angles. y = 93° find x: find y: 3 93°

Similar Triangles For two triangles to be similar: Corresponding angles are congruent. Corresponding sides are proportional. A B C X Y Z Since corresponding angles are congruent and corresponding sides are proportional; the triangles are similar:

Similarity Ratio Similarity ratio is the ratio between corresponding sides of similar shapes. The similarity ratio can be determined two ways: Smallest shape to Largest shape (S  L) Largest shape to Smallest shape (L  S) Calculate ratios for all corresponding sides

Using the Similarity Ratio (from previous slide): The triangles are similar. To solve for a variable on the smaller triangle (x), multiply the corresponding larger side by the (S  L) similarity ratio. x = x 8 x = 4 To solve for a variable on the larger triangle (y), multiply the corresponding smaller side by the (L  S) similarity ratio. y y =6 y = 12

Using Proportions to solve: (from previous slide): The triangles are similar. x y find x: find y: 2

Find the S  L and the L  S similarity ratios, then find x and y. The triangles are similar. S  L : 3 12 x y 20 4 or L  S: or x =20= 5 5 y =4 = find x: find y: 3 Using Proportions:

Overlapping Similar Triangles A B C DE The similarity ratio is 1:2 Drawing the triangles separately can help us find x and y: A B C A D E y 6 x 4 y 6 x y SL SL = LSLS= x =6 (2) x = 12 y =(y + 5) 2y = y + 5 -y y = 5 = = 5 12 find x: find y:

Using proportions: A B C A D E 4 y 6 x y y y = 5 find x: find y: 4