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Your Scaled Measure If you are a quarter of your size. How tall and how wide are you going to be?
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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.