Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent...

Use Similar Polygons

6.3

Similar Polygons• Similar Polygons: all corresponding angles are

congruent and the sides are proportional.

When 2 polygons are similar

The symbol used when 2 figures are similar is: ~When you know 2 figures are similar you must name the corresponding angles in the same order.

Name the corresponding angles, then the ratios of the corresponding sides.

ŸA,ŸDŸB,ŸEŸC,ŸF

DE

AB

EF

BC

DF

AC

Name the corresponding angles, then the ratios of the corresponding sides.

ŸR,ŸWŸS,ŸVŸT,ŸU

WV

RS

ST

VU

WU

RT

Name the corresponding angles, then the ratios of the corresponding sides.

ŸC,ŸMŸD,ŸJŸE,ŸK

MJ

CD

JK

DE

KL

EF

ŸF,ŸL

ML

CF

Name the corresponding angles, then the ratios of the corresponding sides.

ŸP,ŸZŸQ,ŸWŸR,ŸX

ZW

PQ

WX

QR

XY

RS

ŸS,ŸY

ZY

PS

Are the figures named correctly?

yes

Are the figures named correctly?

yes

Are the figures named correctly?

no

A B

C

E

F

G

ABC ~EFG

Are the figures named correctly?

yes

SRQP ~ JKLM

Are the figures named correctly?

no

ABCD ~ EHGF

Scale factor

• The scale factor is the simplified ratio of corresponding sides of a similar polygon

3

2

6

4

3

2

9

6

Determine whether the polygons are similar…then state a similarity statement, and find the scale factor.

yes

„ABC~„FDE„ACB~„FED„BCA~„DEF„BAC~„DFE„CAB~„EFD„CBA~„EDF

Determine whether the polygons are similar…then state a similarity statement.

yes

„ABC~„FDE„ACB~„FED„BCA~„DEF„BAC~„DFE„CAB~„EFD„CBA~„EDF

What is the scale factor of ZWXY to FJHG ?

What is the scale factor of QRST to ABCD?

What is the scale factor of QRST to ZWXY ?

Not similar

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Use the scale factor to find the length of a side.

204

34

3

12

9

x

rscalefactoNM

ED

Cross multiply3(20) = 4x

60 = 4x15 = x

Find x

x

4

12

6 6x = 4(12)

6x = 48

x = 8

Find x

x = 18

Find x

x = 24

Find y

y= 12

Find the scale factor, then find the lengths of the sides, and the perimeter.

factorscale4

3

12

9

x

15

4

3

y

21

4

3

x

y

3x = 4(15)3x = 60x = 20

3y = 4(21)3y = 84y = 28

P= 60

P= 45

Find the scale factor, then find the lengths of the sides, and the perimeter.

factorscale5

3

35

21

255

3 x

205

3 y

x

y

3(25) = 5x75 = 5x15 = x

5y = 3(20)5y = 60y = 12

P= 100 P= 60

z

205

3 z

5z = 3(20)5z = 60z = 12

Worksheet