Lesson 6-2 Similar polygonsSimilar polygonsSimilar polygonsSimilar polygons

Lesson 6-2 DefinitionDefinitionDefinitionDefinition

DE

ABCorresponding Angles are congruent Corresponding sides are proportional

DEFABC ~

(similar to)

DA

EB

FC EF

BC

DF

AC

A B

C

8

12

16

D E

F

15

10 20

15

12 5

4

20

16 5

4

10

8 5

4

The ratio of

Corresponding sides

Scale Factor

is called

(similarity statement)

Two polygons are similar if and only if

Lesson 6-2 ExamplesExamplesExamplesExamples

1) Are the polygons similar? 2( If they are, write a similarity statement

3( and give the scale factor.

1) Check for corresponding angles and sides

FZ

HX

JW

GY

ANGLES SIDES

FJ

ZW

JH

WX

HG

XY

16

20 4

5

12

15

24

30

GF

YZ 20

25

4

5

4

5

4

5

Yes they are ~

2) Similarity statement

JHGFWXYZ ~

3) Scale Factor 4

5

Lesson 6-2

In the diagram, ∆DEF ~ ∆MNP. Find the value of x.

Step1: Set up proportions of the sides .

Step2: Cross multiply and solve .

MP

DF

NP

EF

MN

DE

16

12

2012

9

x

4

3

204

3

x

4

3

20

x 604 x4 4

15x

ExamplesExamplesExamplesExamples

Lesson 6-2

A. Yes, ΔAXE ~ ΔWRT.

B. Yes, ΔAXE ~ ΔRWT.

C. No, the Δ's are not ~.

D. not enough information

Determine whether the pair of figures is similar .

ExamplesExamplesExamplesExamples

Lesson 6-2

A. Yes, ΔTRS ~ ΔNGA.

B. Yes, ΔTRS ~ ΔGNA.

C. No, the Δ's are not ~.

D. not enough information

Determine whether the pair of figures is similar .

ExamplesExamplesExamplesExamples

Lesson 6-2

A. TRAP ~ OZDL

B. TRAP ~ OLDZ

C. TRAP ~ ZDLO

D. TRAP ~ ZOLD

The two polygons are similar. Write a similarity statement.

ExamplesExamplesExamplesExamples

Lesson 6-2

A. a = 1.4

B. a = 3.75

C. a = 2.4

D. a = 2

The two polygons are similar. Solve for a.

ExamplesExamplesExamplesExamples

Lesson 6-2

The two polygons are similar. Solve for b.

A. b = 7.2

B. b = 1.2

C.

D. b = 7.2

ExamplesExamplesExamplesExamples

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Determine whether each pair of figures is similar. Justify your answerDetermine whether each pair of figures is similar. Justify your answer

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Determine whether each pair of figures is similar. Justify your answerDetermine whether each pair of figures is similar. Justify your answer

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Lesson 6-2 Practice and Apply.Practice and Apply. Page 293 Page 293Practice and Apply.Practice and Apply. Page 293 Page 293

Extra PracticeExtra PracticeExtra PracticeExtra Practice

Extra PracticeExtra PracticeExtra PracticeExtra Practice

Extra PracticeExtra PracticeExtra PracticeExtra Practice

Extra PracticeExtra PracticeExtra PracticeExtra Practice

Solve and graph

964 x1)

Extra PracticeExtra PracticeExtra PracticeExtra Practice

2) 3712 x

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3) 32245 x