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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?