6.3 Use Similar PolygonsLearning Target: Students will be able to use proportions to identify similar polygons.

March 31, 2014

Ex 1: Use Similarity Statements• Similar Polygons- two polygons are similar if

corresponding angles are congruent and corresponding side lengths are proportional

In the diagram ΔABC ~ ΔDEF

a) List all pairs of congruent angles.b) Check that the ratios of corresponding side lengths are

equal.c) Write the ratios of the corresponding side lengths in a

statement of proportionality.

A 30

2025

42

2835

F

E

DC

B

Ex 2: Find the Scale Factor• Scale Factor- the ratio of the lengths of two

corresponding sides of two polygons

Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of RSTU and DEFG.

22

18

20

8

F

E

G

D

33

27

30

12

U

T

S

R

3 : 2RSTU ~ DEFG

Ex 3: Use Similar Polygons• In the diagram, ΔABC ~ ΔGHJ. Find the value of x.

18

8 16

12J

H

G12

x

C

B

A AB BCGH HJ

128 16

x

192 8x24x 24BC

Ex 4: Find Perimeters of Similar Figures• Theorem 6.1- Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

• You are constructing a rectangular play area. A playground is rectangular with length 25 meters and width 15 meters. The new play area will be similar in shape, but only 10 meters in length.

a) Find the scale factor of the new play area to the playground.10 : 25 or 2 : 5

b) Find the perimeter of the playground and the play area.Playground = 80 meters

Play Area - 25 80

x 160 5x 32x meters

Ex 5: Use a Scale Factor• In the diagram, ΔMNP ~ ΔRST. Find the length of the

altitude NL.• Find the scale.

• Find NL.

30 320 2

314 2NL

2 42NL

21NL R20 14

S

18L T P

27

N

30

M

Guided Practice• In the diagram, ΔJKL ~ ΔEFG• Find scale factor.

• Find KM.

48 48 9640 40 80

65

635 5KM

5 210KM 42KM

35

40

F

EHG

M48L

K

J

AssignmentPg. 376 #4-24 even