Lesson 13.1 Similar Figures pp. 536-539

Objectives: 1. To define similar polygons. 2. To apply proportions to problems involving similar figures.

Definition Similar polygons are polygons having corresponding angles that are congruent and corresponding sides that are proportional. If ABC and DEF are similar, the proper notation is ABC ~ DEF.

A  D, B  E, & C  F FD CA EF BC DE AB = What exactly does ABC ~ DEF mean? A  D, B  E, & C  F FD CA EF BC DE AB =

A ratio is the comparison of two numbers A ratio is the comparison of two numbers. A proportion is an equation with two equal ratios. To solve a proportion, cross multiply.

. 15 9 5 x Solve = 15 9 5 x = x 15 = 45 3 x =

A′ B′ C′ 8 4 6 A B C 16 8 12 BC C B ′ = AC A AB 2 1 16 8 = AB B A ′ 2 1 12 6 = BC C B ′ 2 1 8 4 = AC C A ′ Therefore ABC ~ A′B′C′.

If the corresponding angles of two polygons are congruent and the corresponding sides are proportional, then you know the two figures are similar.

Practice: Set up a proportion for the following dilation and solve for the missing term. 1. AB = 5, A′B′ = 75, CD = 3. Find C′D′.

Practice: Set up a proportion for the following dilation and solve for the missing term. 2. A′B′ = 20, CD = 12, C′D′ = 8. Find AB.

Practice: If the figures are similar, find the unknown values. 3. 6 4 x

Practice: If the figures are similar, find the unknown values. 4. 10 4 8 3 x y

Practice: If the figures are similar, find the unknown values. 5. 33 55 3 x

Homework pp. 538-539

►A. Exercises Solve each proportion. 3. 63 54 x 6 =

►A. Exercises Find the ratio of the lengths in the right figure (image) to those in the left figure (preimage) for each pair of similar figures. 7. 12 3 8 4 16 2 1

►A. Exercises Given that the figures are similar in each problem, find the length of the indicated sides. 11. 4 3 5 x y 6

►B. Exercises 13. If LPQ ~ RST, what angles are congruent, and what sides are proportional?

►B. Exercises 15. Are congruent triangles also similar?

■ Cumulative Review 21. Find the center of the dilation.

■ Cumulative Review 22. Give the scale factor. A A’ B B’ C C’

■ Cumulative Review 23. If the image of a dilation is congruent to the preimage, then what is the scale factor?

■ Cumulative Review 24. Classify three types of dilations based on scale factors.

25. Find A′B′C′, if P is the center of a dilation with scale . ■ Cumulative Review 25. Find A′B′C′, if P is the center of a dilation with scale . 4 3 ●P