Target: Use proportions to solve problems

involving similar figures.

1. Solve for x:

Similar, congruent, or neither?2. 3.

4. Determine the scale factor for the similar figures.

15

9

20

x

10

1615

24

Word Review Ratio◦ A Fraction

Proportion◦ 2 = Fractions

Scale Factor◦ Model dimension vs actual dimension

8

54

96.9

2.1

15

10

6

4

18:1 18

1

Using Scale Factor: The Scale Factor can be one of the fractions in a proportion

18:1

7 inches18

1

Model

The Real Motorcycle

?

7

How Long is the Real Motorcycle?

Find the height of the tree in Steven’s yard based on the drawing.

Set up the proportion.

Let x = the height of the tree.

Use cross products to solve. 4x = 60 x = 15

The tree is 15 feet tall.

height sSteven'

height stree'

shadow sSteven'

shadow stree'

64

10 x

The parallelograms are similar. Find y.

Write a proportion using corresponding sides.

Use cross products to solve. 6y = 72 y = 12

The missing length is 12 inches.

y

8

9

6

The similar triangles have a scale factor of 3:5. Find a.

Scale factor is the ratio of the sides. Set up a proportion.

Use cross products to solve. 5a = 24 a = 4.8

The missing length is 4.8 yards.

85

3 a

Shannon wanted to measure the height of her house to the tip of its chimney using a mirror.

Set up a proportion using corresponding sides.

Use cross products to solve. 6x = 150 x = 25

Shannon’s house is 25 feet high.

6

30

5

x

Determine the scale factor for each pair of similar figures.

1.

2.

Use proportions to solve for each variable in the similar figures.

3.

4.

24 16

21

21

28

28

Think of a tall object around your home or school. How can you use ratios and proportions to find the height of the object?

Proportions and Similar Figures

Lesson 9

1. Write a ratio for one pair of corresponding sides using numbers.

2. Write a ratio for another pair of corresponding sides using a number and a variable for the missing side.

3. Write a proportion using the ratios of corresponding sides.

4. Solve the proportion.