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Similarity & proportions

Similarity & proportions. Section 7.1 and 7.2 Objective: set up and solve proportions in similar figures What does it mean to be similar/proportional?. Vocabulary. Ratio: the division of two quantities a : b For every “a” you get one “b”.

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Similarity & proportions

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  1. Similarity & proportions Section 7.1 and 7.2 Objective: set up and solve proportions in similar figures What does it mean to be similar/proportional?

  2. Vocabulary • Ratio: the division of two quantities a : b For every “a” you get one “b”

  3. Proportional: corresponding ratios are equal • Similar: same in shape but size may be different (shapes are proportional) Symbol: ~ 7 in 3 in 6 in 14 in 5 in 10 in

  4. Solve Ratios – Cross Multiplying 1. 2.

  5. Example Cookie Recipe • 2 cups flour • 1 tsp baking soda • 1.5 cups sugar • 2 eggs • 1 stick of butter Makes 24 cookies

  6. 1) What is the ratio of flour to cookies? “2 cups of flour for every 24 cookies” 2 : 24

  7. 2) How much flour is needed to make 35 cookies? 3) If you only have 1.5 cups of flour, how many cookies could you make?

  8. 4) How much baking soda, sugar, eggs, and butter would you need to use with 1.5 cups of flour?

  9. Word Problem A baseball team played 154 regular season games. The ratio of number of games they won to the number of games they lost was 5 : 2 How many games did they win? 5(x) + 2(x) = 154 games

  10. Similar Figures • Corresponding angles must be congruent • Sides are PROPORTIONAL • Also known as a “dilation” (enlargement/reduction)

  11. Ex 1) Are the triangles below similar? 70° 70° 6 4.5 4 3 60° 50° 5 60° 50° 7.5

  12. EX. 2 △ABC ~ △PQR Determine the proportional side pairs

  13. Ex 3)△XYZ ~ △XLM Determine the proportional side pairs

  14. Ex 4) What value of x would make ∆ABC ~∆DEF?

  15. Fact: The ratio of a figure & its shadow is proportional the ratio of an object & its shadow at the same time of dayEx 5) Find the height of the tree

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