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Use Similar Polygons 6.3

Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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Page 1: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Use Similar Polygons

6.3

Page 2: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Similar Polygons• Similar Polygons: all corresponding angles are

congruent and the sides are proportional.

Page 3: 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.

Page 4: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

ŸA,ŸDŸB,ŸEŸC,ŸF

DE

AB

EF

BC

DF

AC

Page 5: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

ŸR,ŸWŸS,ŸVŸT,ŸU

WV

RS

ST

VU

WU

RT

Page 6: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 7: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 8: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Are the figures named correctly?

yes

Page 9: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Are the figures named correctly?

yes

Page 10: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Are the figures named correctly?

no

A B

C

E

F

G

ABC ~EFG

Page 11: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Are the figures named correctly?

yes

SRQP ~ JKLM

Page 12: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Are the figures named correctly?

no

ABCD ~ EHGF

Page 13: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Scale factor

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

3

2

6

4

3

2

9

6

Page 14: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 15: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

yes

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

Page 16: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

What is the scale factor of ZWXY to FJHG ?

Page 17: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

What is the scale factor of QRST to ABCD?

Page 18: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

What is the scale factor of QRST to ZWXY ?

Not similar

Page 19: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Page 376

• # 3 - 8

Page 20: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 21: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Find x

x

4

12

6 6x = 4(12)

6x = 48

x = 8

Page 22: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Find x

x = 18

Page 23: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Find x

x = 24

Page 24: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

Find y

y= 12

Page 25: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 26: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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

Page 27: Use Similar Polygons 6.3. Similar Polygons Similar Polygons: all corresponding angles are congruent and the sides are proportional

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