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Warm Up
The geometric mean of 12 and another
number is 30. What is the other number?
Similar Polygons
Geometry
SIMILAR POLYGONS
Two polygons such that their corresponding
angles are congruent and the lengths of
corresponding sides are proportional. The
symbol for “is similar to” is ~
2 Statements We Need to Know
Similarity Statement
• Simply write that the figures are similar
– Be sure to list the corresponding angles in the
same order
Statement of Proportionality
• We write all the corresponding sides as a
proportion
Similar Polygons
Example
Trapezoid ABCD is similar to trapezoid PQRS. List
all the pairs of congruent angles, and write the
ratios of the corresponding sides in a statement
of proportionality.
Similar Polygons
COMET ~ HAIRY
Which angles are congruent?
Write the ratios of the corresponding sides in a
statement of proportionality.
Are the polygons similar?
To Check if the polygons are similar
1. Are the corresponding angles congruent?
2. Are the corresponding side lengths
proportional? (reduce all ratios to see if they
are equal)
Are the polygons similar?
Example
You have a photo 4 in. wide by 6 in. long that
you want to reduce to fit in a frame that is 1.5
in. wide. How long will the reduced photo be?
Example
▲UVW is similar to ▲YXW. Find the value of a.
U
V
a
5
W
12
6.4
X
Y
SCALE FACTOR
If two polygons are similar, then the ratio of
the lengths of two corresponding sides is
called the scale factor.
To find the scale factor, find the reduced
common ratio.
Example
A painting is similar to the wall on which it is
hanging. Calculate the scale factor of the wall to
the painting and find the ratio of their
perimeters.
15 ft
3.2 ft
6 ft
8 ft
Similar Polygons
and their Perimeters
If two polygons are similar, then the ratio of
their perimeters is equal to the ratios of their
corresponding side lengths.
Example
If ABCDE ~ PQRST, find the scale factor of ABCDE
to PQRST and the perimeter of each polygon.
Example
In the diagram, ACDF ~ VWYZ. Find x and y.
A
C
10
Y
12
Z
9
3y - 1
6
F
x
D
W
V