Recognize congruent and similar figures.

Find the scale factor of similar figures.

Similar & Congruent Figures

Solve each proportion.

1.

2.

3. Casey spent $31.50 for 9 tickets to the school carnival. How much would 3 tickets to the school carnival cost?

c

16

15

2

123

5.1 a

Similar: ◦ same shape, different size.

Corresponding Parts: ◦ The angles and sides in similar or congruent figures that match.

Congruent: ◦ Equal in measure (identical twins)

Scale Factor: ◦ The ratio of corresponding sides in two similar figures.

1. Corresponding angles are congruent.

2. The measures of corresponding sides are proportional.

ΔDOT is similar to ΔSUN.Find the scale factor from ΔDOT to ΔSUN.

Write a ratio of corresponding sides.

Simplify the ratio.

The scale factor from ΔDOT to ΔSUN is or 3 : 5.

10

6

5

3

10

6

5

3

Determine whether rectangle CARS is similar to rectangle BIKE. If so, find the scale factor.

All corresponding angles are congruent.

Find the ratio of corresponding heights.

Find the ratio of corresponding lengths.

The corresponding angles are congruent and the corresponding sides have equal ratios so CARS ~ BIKE. The scale factor is or 2 : 3.

3

2

BI

CA

3

2

6

4

EB

SC

32

Consider the two squares above. Are the two squares similar? Explain.

Each angle is 90 , all corresponding angles are equal.⁰ The ratio of any two corresponding sides is:

Yes, the squares are similar. They have a scale factor of 1 : 1.

1

1

5

5

Is Rectangle A similar to Rectangle B? All corresponding angles are equal (90 ).⁰

Find ratio of long sides.

Find ratio of short sides.

Rectangle A is NOT similar to Rectangle B.

7

6

4

3

Ratios not equal so sides are not proportional.

Is Rectangle A similar to Rectangle C?

All corresponding angles are equal (90 ).⁰

Find ratio of long sides.

Find ratio of short sides:

Yes Rectangle A is similar to Rectangle C.

2

1

12

6

2

1

6

3

Ratios are equal so sides are proportional.

1. Find the corresponding sides and corresponding angles to the ones given for the pair of similar figures.

corresponds to ______ P _____ corresponds to _____ A _____ corresponds to _____ R _____ corresponds to _____ K _____

PA

AR

RKKP

3

6

4

8

P A

K R

S U

Y N

Determine the scale factor for each pair of similar figures.

2)

3)

15 35

16 48

1545

What is an example of two congruent figures in your home? What is an example of two similar figures in your home?