1. Lesson 13.1
Similar Figures pp

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

3. 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.

4. 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 =

5. 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.

6. . 15 9 5 x
Solve = 15 9 5 x = x 15 = 45 3 x =

7. 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′.

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

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

10. 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.

11. Practice: If the figures are similar, find the unknown values. 3.6 4 x

12. Practice: If the figures are similar, find the unknown values. 4.10 4 8 3 x y

13. Practice: If the figures are similar, find the unknown values. 5.33 55 3 x

14. Homework pp

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

16. ►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

17. ►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

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

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

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

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

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

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

24. 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