Circle Limit IIIM.C. Escher

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

Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.

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

All the angles are the same

All sides areproportional

Similar Polygons – 2 polygons that have the same shape but not the same size.

Symbol ( ~ ) Corresponding s are . Corresponding sides are Proportional.

Equal Ratios:

** Reduce to the same fraction!!

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

Writing Math

Ex: Order Matters ΔABC ~ ΔXYZ

A

B

C

10

X

Y

Z42

78

BC corresponds to YZ

mB =

mC =

78

60

Find AB:

4 6

8

410

= 6AB AB = 15

410

= 8AC AC = 20Find AC:

Example : Identifying Similar Polygons

Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

rectangles ABCD and EFGH

Example 3

A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.

Example 3 Continued

1.25(36.25) = x(9) Cross Products Prop.45.3 = 9x Simplify.

5 x Divide both sides by 9.

The length of the model is approximately 5 inches.

Ex. 2: Are the following polygons similar?

1in

B C

DA

K L

MJ

2in

2in

4in 4in

1in

2in

1in

2in

1) Check to see if all s are ?

2) Check the ratio of all corresponding sides?

120

80