Lesson 5-2

Similar Polygons

Lesson 5-2: Similar Polygons 1

Similar Polygons

Definition:

Two polygons are similar if: 1. Corresponding angles are congruent.

2. Corresponding sides are in proportion.

Two polygons are similar if they have the same shape not necessarily have the same size.

Scale Factor:

The scale factor is the ratio between a pair of corresponding sides.

2 Lesson 5-2: Similar Polygons

Naming Similar Polygons

When naming similar polygons, the vertices (angles, sides) must be named in the corresponding order.

If ABCD A P PQRS B Q

;

AB PQ



BC QR



CD RS



AD PS C

A

R

;

D

B

S

P Q D C S Lesson 5-2: Similar Polygons 3 R

Example-

A The two polygons are similar. Solve for x, y and z.

20 15

D

y

E

10 x

H

5

B

Step1:

Write the proportion of the sides.

30

AD EH



DC HG

C F

z



BC FG



AB EF

G

Step 2:

Replace the proportion with values.

15

x y

5 30

z

 20 10

Step 3:

Find the scale factor between the two polygons.

Note:

The scale factor has the larger quadrilateral in the numerator and the smaller quadrilateral in the denominator.

Step 4:

Write separate proportions for each missing side and solve.

15

x

 2 1 

x

 7.5

y

5  2 1 

y

 10 30

z

 2 1 

z

 15 Lesson 5-2: Similar Polygons 4

Example:

If 

ABC ~



ZYX, find the scale factor from



ABC to



ZYX.

Scale factor is same as the ratio of the sides. Always put the first polygon mentioned in the numerator. C

10

AB ZY  18 9  2 1 B X

5

Y

14 18 7 9 The scale factor from



ABC to



ZYX

is

2/1

.

A What is the scale factor from 

ZYX to



ABC?

Z

½

5 Lesson 5-2: Similar Polygons