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Proportions & Similar Figures

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Proportions A proportion is an equation that shows two equivalent ratios. NS 1.3

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Getting smaller Find the missing value in each proportion. x 2 2 ÷ 3 3 Getting bigger

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Find the missing value in the proportion. 1. Sometimes the problem is easy to solve by using multiplication or division. x 2 6 x = 6

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2. NS 1.3 use cross products (cross x) to create an equation that you can solve. 4 x = 3 8 simplify 24 4x4x = How do you solve the equation? ÷ 4÷ 4 x = 6

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3. Use cross products to solve the problem. 6 x = 4 9 simplify 36 6x6x = solve the equation ÷ 6÷ 6 x = 6

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4. Use cross products to solve the problem. 10 x = 5 8 simplify 40 10 x = solve the equation ÷ 10 x = 4

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5. 6.

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7.8.

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Solving PROPORTIONS (when you have similar figures)

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What are similar figures? SIMILAR figures have… –Congruent angles –PROPORTIONATE side lengths. –What does proportionate mean ?

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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)

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3 cm x 4 cm 12 cm

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8 cm 32 cm 28 cm x

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24 ft x 2 ft 6 ft

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10 in 6 in __ in 2 in

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2 mm 7 mm x

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3 in 8 in x 6 in

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1 m 10 m __ m 5 m

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4 cm x 8 cm 16 cm 20 cm 10 cm

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12 cm x 6 cm 8 cm 18 cm 9 cm

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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.

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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?

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