Similar Polygons

Vocabulary

• Polygon: Consists of a sequence of consecutive line segments in a plane, placed and to end to form a simple closed figure.

• Similar Polygons: Polygons that have the same shape but not necessarily the same size

• Corresponding Parts: Parts of similar figures that “match”.

• Corresponding Angles are congruent

• Corresponding side measurements are proportional.

• Scale Factor: The ratio of the lengths of two corresponding sides of two similar polygons.

• The ratio of the measures of a pair of corresponding sides is the scale factor

• The perimeters have a ratio that equals the scale factor.

• The areas have a ratio that equals the square of the scale factor.

Key ConceptWORDS: If two polygons are similar, then• Their corresponding angles are CONGRUENT, or

have the same measurement.• The measures of their corresponding sides are

proportional

MODEL

A ZX

Y

C

B

SYMBOLS:

• Determine whether rectangle HJKL is similar to rectangle MNPQ. Explain

H

Q

3 6

P

NM

L K

J

107

Given that polygon WXYZ ~ polygon ABCD, find the missing measurement.

12

15

D CYZ

X

WB

A

10

13m

24

Using Scale Factor to Write and Equation

A length on polygon WXYZ is

3/2 times as long as ….

corresponding length on polygon ABCD

Let m represent the measure of XY

m = 3/2 · 12

Find the missing measure

• WZ

• AB

• Given rectangle LMNO ~ rectangle GHIJ, find the missing measure.

4

2

J

G

I

H

O

L

N

M

m

3

Ratios of Similar Figures

WORDS: If two figures are similar with a scale factor of a/b, then the perimeters of the figures have a ratio of a/b

MODEL:

a b

Figure A Figure B

Triangle LMN is similar to triangle PQR. If the perimeter of ∆ LMN is 64 units, what is the perimeter of ∆ PQR?

L

M N R Q

P

1824

A)108 units

B) 96 units

C) 48 units

D)36 units

Rectangle KLMN is similar to rectangle TUVW. If the perimeter of rectangle KLMN is 32 units, what is the perimeter of rectangle TUVW?

a) 128 units

b) 96 units

c) 64 units

d) 40 units