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Objectives: write ratios/proportions to find dimensions from scale drawings

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Objectives: write ratios/proportions to find dimensions from scale drawings

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  1. Section 8-1 Ratios and Proportions SPI 31A: identify corresponding parts of congruent geometric figuresSPI 32C: determine congruence or relations between triangles or quadrilaterals given a diagramSPI 22B: apply ratio and proportion to solve real-world problems • Objectives: • write ratios/proportions to find dimensions from scale drawings Vocabulary Ratio: comparison of two numbers by division Scale Drawing: scale compares each length in the drawing to the actual length. Proportion: an equation that states two ratios are equal. Cross-Product Property: shortcut for finding a variable when one fraction is set equal to another.

  2. Ratio (comparison of 2 numbers by division) The ratio of two quantities a and b, can be written as: a to b a:b Example What is the ratio of girls to boys if there are 13 girls and 22 boys? 13 to 22 13:22

  3. Real-world and Ratios In the plains of Africa, zoologist tagged zebras to discover that there exists 178 female zebras to 148 male zebras. What is the ratio of male to total number of zebra? There are 148 male zebras. There is a total of 326 zebras. The ratio is 148 to 326 148:326 Always reduce to lowest terms 74 to 163 74:163

  4. Real-world Connection to Ratios Photography: A photo that is 8 in wide and 5 1/3 inches highis enlarged to a poster that is 2 ft wide and 1 1/3 ft high. What is the ratio of the width of the photo to the width of the poster? 8 in 24 in 1 3 8 in 2 ft Width of photo Width of poster = = = The ratio of the width of the photo to the width of the poster is 1:3 or 1/3.

  5. Proportions (an equation that states two ratios are equal) Cross Products of Proportions (Use ONLY when one ratio or fraction equals another) Use Multiplication Property of Equality to Solve Proportions

  6. Properties of Proportions Properties of Proportions govern when two equations are equivalent

  7. Use Cross-Products to Solve the Proportions Do Now 1. Solve the proportion: 2. Solve the proportion: Distributive Property Simplify SPE Simplify SPE Simplify

  8. Setting up to Write a Proportion If people could jump as high as a flea, how high could a person, that is 5 feet tall jump if a flea that is .125 inches tall can jump to a height of 13 inches? Jump height Tallness 13 .125 x 5 = Answer the question A person could jump to a height of 520 feet.

  9. Real-world Connection and Scale Drawings Try It! The bedroom in the scale drawing is 7/8 in by 5/8 in. Find the actual dimensions of the bedroom. 1 in 16 ft 1 in 16 ft Drawing length (in) Actual length (ft) 7/8 in x 5/8 in y = = y = (5/8)(16) x = (7/8)(16) The actual size of the bedroom is 14 ft by 10 ft y = 10 x = 14

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