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

DEAB

EFBC

DFAC

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

ŸR,ŸWŸS,ŸVŸT,ŸU

WVRS

STVU

WURT

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

ŸC,ŸMŸD,ŸJŸE,ŸK

MJCD

JKDE

KLEF

ŸF,ŸL

MLCF

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

ŸP,ŸZŸQ,ŸWŸR,ŸX

ZWPQ

WXQR

XYRS

ŸS,ŸY

ZYPS

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

32

64

32

96

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.

2043

43

129

x

rscalefactoNMED

Cross multiply3(20) = 4x

60 = 4x15 = x

Find x

x4

126

6x = 4(12)6x = 48x = 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.

factorscale43

129

x15

43

y21

43

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.

factorscale53

3521

2553 x

205

3 y

x

y

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

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

P= 100 P= 60

z

2053 z

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

Worksheet