7.3 Similar Polygons

Slide 7-1
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Objectives

1.

Identify Similar Polygons.

2.

Use Similar Polygons to Solve Applications.

7.3 Similar Polygons

Multiple Choice

Solve the proportion:

• 15

• 5

• 10

• 12

Multiple Choice

Solve the proportion.

• k=5

• k=3.3333333

• k=60

• k=90

Slide 7-2

Similar Polygons

Similar figures have the same shape but not
necessarily the same size. We will abbreviate “is
similar to” with the symbol ∼.

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Slide 7-3

Similar Polygons

We write a similarity statement with corresponding
vertices in order, the same way we write a
congruence statement. When three or more ratios are
equal, we can write an extended proportion.

The proportion

is an extended

proportion.

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Slide 7-4

ExampleUnderstanding Similarity and

Using Extended Proportions

a. What are the pairs of congruent angles?
Use the order of the vertices in the similarity
statement ΔMNP ∼ ΔSRT to write pairs of congruent
angles.
∠M ≅∠S, ∠N ≅∠R, and ∠P ≅∠T

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Slide 7-5

ExampleUnderstanding Similarity and

Using Extended Proportions

b. What is the extended proportion for the ratios of
corresponding sides?
Since ΔMNP ∼ ΔSRT, we know that corresponds to
so is a ratio of corresponding sides the same is true
for

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Slide 7-6

Scale Factor

A scale factor is the ratio of corresponding linear
measurements of two similar figures. The ratio of
the lengths of corresponding sides and , or
more simply stated, the ratio of corresponding sides,
is

so the scale factor is 5:2.

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Slide 7-7

ExampleDetermining Similarity Using

Scale Factors (a)

For the figures in a and then in b, answer Part 1and
Part 2.
Part 1 Are the polygons similar?
Part 2 If they are, write a similarity statement and
give the scale factor.
Solution
Part 1: Identify pairs of
congruent angles.
∠J ≅∠T, ∠K ≅∠U, ∠L ≅∠V, and ∠M ≅∠W

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Slide 7-8

ExampleDetermining Similarity Using

Scale Factors (a)

Solution
Compare the ratios of
corresponding sides.

PART 2 Corresponding sides are not proportional
since the scale factors are not the same, so the
polygons are not similar.

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Slide 7-9

ExampleDetermining Similarity Using

Scale Factors (b)

For the figures in a and then in b, answer Part 1and
Part 2.
Part 1 Are the polygons similar?
Part 2 If they are, write a similarity statement and
give the scale factor.
Solution
Part 1: Identify pairs of
congruent angles.
∠A ≅∠D, ∠B ≅∠E, and ∠C ≅∠F

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Slide 7-10

ExampleDetermining Similarity Using

Scale Factors (b)

Solution
Compare the ratios of
corresponding sides.

PART 2 Yes; ΔABC ∼ ΔDEF and the scale factor is
4:5.

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Slide 7-11

ExampleUsing Similar Polygons to Find

Unknown Values

MULTIPLE CHOICE: ABCD ∼EFGD. What is
the value of x?
a. 4.5b. 5
c. 7.2

d. 11.25

Solution
Use the similarity statement to write a proportion.

Copyright © 2014 Pearson Education, Inc.

Slide 7-12

ExampleUsing Similar Polygons to Find

Unknown Values

MULTIPLE CHOICE: ABCD ∼EFGD. What is
the value of x?
a. 4.5b. 5 c. 7.2 d. 11.25

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The value of x is 5. The
correct answer is b.

Slide 7-13

ExampleUsing Similarity

Your class is making a rectangular poster for a rally.
The poster’s design is 6 in. in width by 10 in. in
length. The space allowed for the poster is 4 ft in
width by 8 ft in length. What are the dimensions of
the largest poster that will still fit in the space?

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Slide 7-14

ExampleUsing Similarity

Solution
Step 1. Determine whether the width or the length
will fill the space first.
Width: 4 ft = 48 in.
How many 6 in. will fit in 4 ft?
Length: 8 ft = 96 in.
How many 10 in. will fit in 8 ft?
The design can be enlarged at most 8 times (the
smaller of the two quotients).

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Slide 7-15

ExampleUsing Similarity

Solution
Step 2. The greatest width is 48 in., so find the
length.

The largest poster that will fit is 48 in. by 80 in. or
4 ft by 20/3 ft or 4 ft by 6 2/3ft.

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