Similar - Two figures are similar figures if they have the same shape but they may not be the same size.

The symbol ~ means similar.

Corresponding parts of figures are sides or angles that have the same relative position.

A

CB

D

FE

∆ABC ~ ∆DEF

That means A corresponds to

D

B corresponds to

E

C corresponds to

F

AB corresponds to

DE

BC corresponds to

EF

AC corresponds to

DF

Given: ABCD ~ WXYZ name the corresponding angles and the corresponding sides.

A corresponds toB corresponds to

W

X

C corresponds to

Y

D corresponds to

Z

AB corresponds toBC corresponds toCD corresponds toAD corresponds to

WX

XY

YZ

WZ

Corresponding angles of similar figures are congruent.

The ratios of the lengths of corresponding sides of similar figures are equal.

Remember -

Angles equal and side lengths proportional.

Are the following rectangles similar?

R S

TU

4 cm

12 cm

J K

L M

2 cm

6 cm

Set up a proportion using the ratios of the corresponding sides.

R S

TU

4 cm

12 cm

J K

L M

2 cm

6 cm

RS

RU

KM

ML

= 4

12

2

6=

Cross Multiply 24 24=

Therefore, they are similar rectangles.

Congruent Figures - Two figures are congruent if they have the same shape and the same size.

Corresponding parts of congruent figures are found the same way as for similar figures.

The symbol for congruent is

ABCD WXYZ

Remember - Angles and sides are equal.

ABCD WXYZ

A B

CD

W

X

Y

Z

12 m

18 m

10278

How long is AB?What is the measurement of Y?