This document discusses similar polygons and scale factors. It provides examples of similar polygons where the corresponding angles are equal but the sides are proportional. It explains that the scale factor is the ratio of corresponding sides between the similar polygons. The scale factor can be used to determine missing side lengths. It concludes by stating that the ratio of perimeters of similar polygons is equal to their scale factor.

1. Circle Limit III
M.C. Escher
Section 7-2 3108.4.37
Jim Smith
JCHS

2. Similar figures look alike but one is a smaller
version of the other. Like Dr. Evil and Mini-Me.
It wouldn’t make much sense to make a drawing
of this ship the actual size of the ship.

3. Just like congruent polygons, the
corresponding
angles in similar polygons must be
congruent.

4. A X
C
D
B W
Z Y
A = 80° B = 30° Z = 170°
W = ___ X = ___ D = ___
80° 30° 170°

5. The sides are a little different.
They must be PROPORTIONAL.
A X
C
D
B
W
Z Y
AB = BC = CD = DA
WX XY YZ ZW

6. This means I should be able to multiply each side
of the smaller polygon by the same number and
get it’s corresponding side on the bigger polygon.
4
4x2 = 8
5
5x2 = 10
2
2x2 = 4
3
3x2 = 6

7. The SCALE FACTOR is the ratio
of the corresponding sides
SMALL BIG
BIG SMALL
or

8. What is the scale factor of these
polygons?
10
4
X 7
Y
8
Z
6
Scale Factor = 10
4
= 5
2

9. 4
7
Y
Z
10
X
8
6
10
4
= 5
2
Use the scale factor to find the other sides
5 6
2 Z
=
5z = 12
z = 12 = 2.4
5
SF =
5 X
2 7
2x = 35
x = 35 = 17.5
2
= 5 8
2 Y
5y = 16
y = 16 = 3.2
5
=

10. The ratio of the perimeters of
2 similar polygons is the same
as the scale factor.
5 3
4
5

11. With similar polygons:
Corresponding angles are
Corresponding sides are
What is a scale factor
How would we test for similarity
Compare similarity and congruency