warm-up x = 18 t = 3, -7 u = ± 7. 7-2 similar polygons i can use the definition of similar polygons...

WARM-UP

x = 18

t = 3, -7

u = ±7

7-2 Similar Polygons

I CAN

•Use the definition of similar polygons to determine if two polygons are similar

•Determine the similarity ratio between two polygons.

•Create a similar figure using a similarity ratio

Figures that are similar (~) have the same shape but not necessarily the same size.

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Review Congruent Triangles Does AAA prove triangles are congruent?

What would AAA prove?

Two polygons are similar if and only if:

1. ALL corresponding angles are congruent

2. ALL corresponding sides are proportional.

Is PQR similar to ZYX ?

P

Q

R X

Y

Z

9 1015 6

1218

< Q < Y< P < Z

} Given

< R < X 3rd Angle Theorem

Are ratios of corresponding sides equal?Are corresponding angles equal?

YES

PQ = 9 = 3ZY 6 2

PR = 18 = 3ZX 12 2

RQ = 15 = 3YX 10 2 YES

A similarity ratio is the ratio of the lengths of

the corresponding sides of two similar polygons.

The similarity ratio of ∆ABC to ∆DEF is , or .

The similarity ratio of ∆DEF to ∆ABC is , or 2.

How is the similarity ratio and scale factor related?

The similarity ratio is the reciprocal of the scale factor!

Similarity Statement

PQR ~ ZYX

“is similar to”

The similarity ratio of triangle PQR to triangle ZYX is 9 to 6 or 9 = 3 6 2

The similarity ratio of triangle ZYX to triangle PQR is 6 to 9or 6 = 2 9 3

P

Q

R X

Y

Z

9 1015 6

1218

Is ABC similar to KLJ ?

A

B

C

2 8

5

< A < K< B < L

} Given

< C < J 3rd Angle Theorem

Are ratios of corresponding sides equal?Are corresponding angles equal?

YES

AB = 2 = 1KL 4 2

BC = 8 = 4JL 18 9

Example

K

L

J

10

4

18

NO, the sides are not proportional!

Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.

Writing Math

Application Problem

You are building a model of the school. The similarity ratio of the model to the actual building is 1 400

If the actual building is 1,000 ft wide, how wide is the model?

Model =Actual

1 = x400 1,000

x = 2.5 feet wide

Your Turn

The ratio of a model scale die cast motorcycle is 1:18. The model is 5 ¼ inches long. What is the length of the actual motorcycle in feet and inches?

7 ft 10 ½ in