lesson 13.1 similar figures pp. 536-539

Lesson 13.1Similar Figures

pp. 536-539

Lesson 13.1Similar Figures

pp. 536-539

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

involving similar figures.

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

involving similar figures.

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

DefinitionDefinitionDefinitionDefinition

What exactly does ABC ~ DEF mean? What exactly does ABC ~ DEF mean?

A D, B E,& C F

A D, B E,& C F

FDFDCACA

EFEFBCBC

DEDEABAB

====

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

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

..151599

55xx

SolveSolve ==

33xx ==

4545xx1515 ==151599

55xx

==

AA BB

CC

1616

88 1212A′A′ B′B′

C′C′

88

44 66

2211

161688

====ABAB

BBAA ′′′′

2211

8844

====ACAC

CCAA ′′′′

2211

121266

====BCBC

CCBB ′′′′

BCBCCCBB ′′′′

==ACAC

CCAA ′′′′==

ABABBBAA ′′′′

Therefore ABC ~ A′B′C′.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.

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. 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: 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.

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

33

66

44

xx

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

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

101044

88

33

xxyy

Practice: If the figures are similar, find the unknown values.5.

Practice: If the figures are similar, find the unknown values.5.

3333

5555

33

xx

Homeworkpp. 538-539Homeworkpp. 538-539

►A. ExercisesSolve each proportion.

3.

►A. ExercisesSolve each proportion.

3.63635454

xx66

==

►A. ExercisesFind the ratio of the lengths in the right figure (image) to those in the left figure (preimage) for each pair of similar figures.

7.

►A. ExercisesFind the ratio of the lengths in the right figure (image) to those in the left figure (preimage) for each pair of similar figures.

7.

1212 33

88

441616

2211 44

►A. ExercisesGiven that the figures are similar in each problem, find the length of the indicated sides.

11.

►A. ExercisesGiven that the figures are similar in each problem, find the length of the indicated sides.

11. 44

33 5555 33

44

xxyy

66

►B. Exercises13. If LPQ ~ RST, what angles

are congruent, and what sides are proportional?

►B. Exercises13. If LPQ ~ RST, what angles

are congruent, and what sides are proportional?

►B. Exercises15. Are congruent triangles also

similar?

►B. Exercises15. Are congruent triangles also

similar?

■ Cumulative Review21. Find the center of the dilation. ■ Cumulative Review21. Find the center of the dilation.

■ Cumulative Review22. Give the scale factor.■ Cumulative Review22. Give the scale factor.

AA

BB C’C’B’B’

A’A’

CC

■ Cumulative Review23. If the image of a dilation is

congruent to the preimage, then what is the scale factor?

■ Cumulative Review23. If the image of a dilation is

congruent to the preimage, then what is the scale factor?

■ Cumulative Review24. Classify three types of

dilations based on scale factors.

■ Cumulative Review24. Classify three types of

dilations based on scale factors.

■ Cumulative Review25. Find A′B′C′, if P is the

center of a dilation with scale .

■ Cumulative Review25. Find A′B′C′, if P is the

center of a dilation with scale .

●P ●P

4433