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8.2 Problem Solving in Geometry with Proportions

8.2 Problem Solving in Geometry with Proportions. Additional Properties of Proportions. If , then If , then. Using Properties of Proportions. Tell whether the statement is true. true. Not true—c + 3 should be c + 4. In the diagram .

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8.2 Problem Solving in Geometry with Proportions

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  1. 8.2 Problem Solving in Geometry with Proportions

  2. Additional Properties of Proportions • If , then • If , then

  3. Using Properties of Proportions • Tell whether the statement is true. true Not true—c + 3 should be c + 4.

  4. In the diagram . Find the length of BD. A 30 16 • AB = AC16 = 20* • BD CE X 10 • 160 = 20X • 8 = X • Find the length of AC by • Subtracting 10 from 20. B C x 10 D E

  5. In the diagram • Solve for DE. A 5 2 2 = 5 X 15 = 2x 7.5 = x D B 3 E C

  6. Geometric mean • The geometric mean of two positive numbers a and b is the positive number x such that • Find the geometric mean of 8 and 18. 8(18) = 144 √144 = 12

  7. Geometric Mean • Find the geometric mean of 5 and 20. • The geometric mean of x and 5 is 15. Find the value of x. So, the square root of 5x = 15 So, 152 = 5x 225 = 5x 45 = x

  8. Different perspective of Geometric mean • The geometric mean of ‘a’ and ‘b’ is √ab • Therefore geometric mean of 4 and 9 is 6, since √(4)(9) = √36 = 6.

  9. Geometric mean • Find the geometric mean of the two numbers. • 3 and 27 √(3)(27) = √81 = 9 • 4 and 16 √(4)(16) = √64 = 8 • 5 and 15 √(5)(15) = √75 = 5√3

  10. A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The titanic itself was 882.75ft long. How wide was it? length width Scale Model = 107.5 = 11.25 Actual Titanic 882.75 x 107.5x = 9930.9375 x ≈ 92.38

  11. Homework • 8.2 • P. 468-471 • 10-28E • 29-33All • 38-40 All • 44-46 All

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