Scale Factor of Similar Figures

Finding the Scale Factor Finding Dimensions with Scale Factor

Irma Crespo 2010

Warm Up What are the two things you need to show

if a pair of polygons is similar?

a) side lengths and angles are identical

b) top and bottom are parallel

c) corresponding angles are equal and the ratio of corresponding side lengths is the same

d) corresponding angles are equal and the corresponding side lengths are the same

Your Scaled Measure If you are a quarter of your

size. How tall and how wide are you going to be?

Scale Factor Scale factor is the ratio of the lengths of the

corresponding sides of similar polygons.

3

L M

O N6

J

G2I

H

4

64

=32

LOGI

= NOJI

= MNHJ

= MLHG

64

= 32

=

32

The Scale Factor

Find the Scale Factor Given that the rectangles are similar, what is

the scale factor?

10 in

6 in

25 in

15 in

a) 1.5

b) 2.5

c) 5.5

d) 19.5

HINTPick a pair of

corresponding side lengths.

Find the Scale Factor

C

A

B

DE

60.25 m

162 m

40 m

320 m

Triangle ABD and triangle ACE are similar.

a)

b)

c)

d)

160241

16081

80120

32

Using Scale Factor Scale factor is used to enlarge or to reduce the size

of an image of the original figure. A scale factor greater than 1 enlarges the size of an

image of the original figure. A scale factor less than 1 reduces the size of an

image of the original figure. A scale factor is multiplied to each corresponding

side length of the original figure.

Scale Factor: Enlarge or Reduce? Scale Factor: ¾ Scale Factor: 5 Scale Factor: .99 Scale Factor: 1.98 Scale Factor: 2 Scale Factor: 8/3

reduceenlargereduceenlargeenlargeenlarge

Finding Dimensions with Scale Factor

Multiply the scale factor to each side length of the original figure.

Scale Factor Greater Than 1The Scale Factor

Multiply to each side length of the original figure.

32

Given:

J

G2I

H

4

original

32

L M

O N

copy

= 62

=

6

3

2( 32

)

4( 32

) = 122

=

6

3

Scale Factor Less Than 1The Scale FactorGiven: 1

9

= 59

= 69

=

copyoriginal

5 8

6

23

5( 19

)

=

6( 19

)

8( 19

) 89

59

23

89

19

Multiply to each side length of the original figure.

Find the Dimension If a rectangle has a LENGTH of 6 cm and

WIDTH of 2 cm, using a scale factor of 5, what would the new dimensions of the rectangle be?

a) LENGTH = 11 cm; WIDTH = 7 cm

b) LENGTH = 30 cm; WIDTH = 10 cm

c) LENGTH = 10 cm; WIDTH = 6 cm

d) LENGTH = 12 cm; WIDTH = 1 cm

Find the Dimension

18

8

108

With scale factor: 3,4

what are the measurements of its similar polygon?

a)

b)

c)

d)

66

7.5

13.5

16

36

2016

6

4.522

59

93

Take note of these… When finding the scale factor of similar polygons,

compute for the ratio of corresponding side lengths. A scale factor greater than 1 enlarges the size of an

image of the original figure. A scale factor less than 1 reduces the size of an

image of the original figure. When finding dimensions of an image of the

original figure, scale factor is multiplied to each corresponding side length of the original figure.

Exit Slip Make up a scale factor problem with your

solution. You can either create a problem in finding the

scale factor or finding dimensions. This is individual work and you get 2 extra credit

points. Don’t forget to write your name and submit it

before leaving class.

Practice WorksheetComplete the practice worksheet.

Work with a partner or on your own.

Submit completed worksheet for grading.

Solutions are discussed the next day.

Problem Solving Worksheet

Main Resources• Math Connects: Concepts, Skills, and Problem

Solving; Teacher Edition; Course 3, Volume 1Columbus:McGraw-Hill, 2009.

• PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of

Education. Winter 2010.