proportions & similar figures. proportions a proportion is an equation that shows two equivalent...

Proportions & Similar Figures

ProportionsA proportion is an equation that shows two equivalent ratios.

5

1

10

2

NS 1.3

12

9

4

x

Getting smaller

Find the missing value in each proportion.

5

1

10

x

x 2

x 2

2

÷ 3

÷ 3

3

Getting bigger

Find the missing value in the proportion.

4

3

8

x1. Sometimes the problem is easy to solve by using multiplication or division.

x 2

x 2

6

x = 6

4

3

8

x2. NS 1.3

use cross products (cross x) to create an equation that you can solve.

4 • x = 3 • 8 simplify

244x = How do you solve the equation?÷ 4

x = 6

x

4

9

63.

Use cross products to solve the problem.

6 • x = 4 • 9 simplify

366x = solve the equation÷ 6

x = 6

x

5

8

104.

Use cross products to solve the problem.

10 •

x= 5 • 8 simplify

4010x = solve the equation

÷

10x = 4

6

5

30

x5.

10

x

6

36.

9

15

x

57.

x

27

6

38.

Solving PROPORTIONS

(when you have similar figures)

What are similar figures?

• SIMILAR figures have…– Congruent angles– PROPORTIONATE side lengths.

– What does proportionate mean?

2 in

6 in

4 in

__ in

1.) Match up the similar sides. tops 4 2 left sides 6 x

2.) Make into fractions and an equation.

3.) Solve.

(a proportion)

3 cm x

4 cm

12 cm

8 cm

32 cm

28 cm

x

24 ft

x

2 ft

6 ft

10 in

6 in

__ in

2 in

2 mm

7 mm

7 mmx

3 in

8 in

x6 in

1 m

10 m

__ m

5 m

4 cm

x

8 cm

16 cm

20 cm10 cm

12 cm

x

6 cm

8 cm

18 cm

9 cm

x

24 ft

5 ft

8 ft

You can find proportions in word problems, too…

If a Johnny is 5ft tall and casts a shadow of 8ft, how tall is a tree

that casts a 24ft shadow? Set up a proportion to solve.

A map has a scale of 1 in : 4 mi. If Merced and Atwater are 2 inches apart on the map then how far apart are the cities?