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Similarity Ratios and Proportions

Similarity Ratios and Proportions. Section 7.1. Ratio. Ways to write a ratio:. Be sure to SIMPLIFY!. Comparison of two quantities. Example. 4 to 18(12) = 4 to 216 = 1 to 54. 4:216 = 1:54. 4 = 1 216 54.

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Similarity Ratios and Proportions

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  1. SimilarityRatios and Proportions Section 7.1

  2. Ratio Ways to write a ratio: Be sure to SIMPLIFY! Comparison of two quantities

  3. Example 4 to 18(12) = 4 to 216 = 1 to 54 4:216 = 1:54 4 = 1 216 54 A scale model of a car is 4” long. The actual car is 18’ long. What is the ratio of the length of the model to the length of the car?

  4. An Equation Proportion A statement that two ratios are equal Extended Proportion: When three or more ratios are equal

  5. Cross-Product Property Means Extremes The product of the extremes is equal to the product of the means

  6. Examples…solve the following proportions 1) 2 : 5 = n : 35 2) 3) 4) x + 1 : 3 = x : 2

  7. Solving Proportions • Use the cross product property to solve for variables in a proportion

  8. Solving an extended proportion • Choose two ratios to work with first in order to solve for a variable • Use substitution and then solve for the other variable using cross product

  9. Another example!

  10. Properties of proportions: Cross Product Property Reciprocals Exchange the means Adding 1 to each side Given: The following is true: 1) 2) 3) 4)

  11. Writing equivalent proportions • Given

  12. Write four true statements given:

  13. Similarity Section 7.2

  14. Similar • Two figures with the same shape that have: • Corresponding angles congruent • Corresponding sides proportional

  15. Similarity Ratio = 2” 1 The ratio of the lengths of corresponding sides

  16. To determine if two figures are similar Check that corresponding angles are congruent and all corresponding sides have an equal similarity ratio

  17. Using Similar Figures Find the missing angles and side lengths given LMNP~QRST

  18. Solve for x and y given LMNO~QRST

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