Transcript PROP Lesson 09 Luke - Sweet Home School District

Target:
Use proportions to solve problems
involving similar figures.
1.
Solve for x:
x
9

20 15
Similar, congruent, or neither?
2.
4.
3.
Determine the scale factor for the similar figures.
10
15
16
24

Ratio
◦ A Fraction

Proportion
◦ 2 = Fractions

9
4
5
8
1 .2
9 .6
4 10

6 15
Scale Factor
◦ Model dimension vs actual dimension
1:18
1
18
1:18

The Scale Factor can be one of the fractions in a proportion
Model
1 7

18 ?
The Real Motorcycle
7 inches
How Long is the
Real Motorcycle?
Find the height of the
tree in Steven’s yard
based on the drawing.

Set up the proportion.
tree' s shadow
tree' s height

Steven' s shadow Steven' s height

Let x = the height of the tree.

Use cross products to solve.

The tree is 15 feet tall.
10 x

4 6
4x = 60
x = 15
The parallelograms are similar. Find y.

Write a proportion using
corresponding sides.

Use cross products to solve.

The missing length is 12 inches.
6 8

9 y
6y = 72
y = 12
The similar triangles have a scale factor of 3:5. Find a.

Scale factor is the ratio of the sides.
Set up a proportion.
3 a

5 8

Use cross products to solve.
5a = 24
a = 4.8

The missing length is 4.8 yards.
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.

Shannon’s house is 25 feet high.
x 30

5 6
6x = 150
x = 25
Determine the scale factor for each pair of similar figures.
1.
21
28
21
28
2.
24
16
Use proportions to solve for each variable in the similar figures.
3.
4.
Think of a tall object around your home or school. How
can you use ratios and proportions to find the height of
the object?
Lesson 9
Proportions and Similar Figures
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.