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8.2 Problem Solving in Geometry with Proportions

8.2 Problem Solving in Geometry with Proportions. Warm-Up. 1) ∆ ABC ≅ ∆ HIJ. Name three pairs of congruent sides. 2) Solve each proportion. a) 3 = x b) 2 = 8 c) x = 1 4 8 x 24 9 3. ?s. Additional Properties of Proportions. If , then

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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. Warm-Up • 1) ∆ ABC ≅∆HIJ. Name three pairs of congruent sides. • 2) Solve each proportion. • a) 3 = x b) 2 = 8 c) x = 1 4 8 x 24 9 3

  3. ?s

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

  5. Using Properties of Proportions • Tell whether the statement is true.

  6. In the diagram . Find the length of BD. A 30 16 B C x 10 D E

  7. In the diagram • Solve for DE. A 5 2 D B 3 E C

  8. Practice • P. 468-470 #9-16, 23-28, 33, 34

  9. Dilations • Dilation—transformation wherein the figure is enlarged or reduced by a set amount • The amount is referred to as the scale factor 6 3

  10. a) Identify the Dilation b) Find the scale factor c) Solve for the variables A 25 B A’ B’ x 8 8 y C’ D’ 10 C z D 10

  11. Practice • P. 509-511 #8-10, 20-21

  12. Warm-Up • 1) Identify the dilation and find the scale factor. Then, find the values of the variables. • 2) Find the measures of the angles: M M’ x 18 Q’ 12 Q 20 y 15 N’ V N 61° U W 58° X

  13. ?s

  14. It’s Lean, It’s Green, It’s… • 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. • Solution: 12

  15. Quick Practice • Find the geometric mean of 5 and 20. • The geometric mean of x and 5 is 15. Find the value of x.

  16. Another Way to Solve • The geometric mean of ‘a’ and ‘b’ is √ab • Using this method, find the geometric mean of 4 and 9 • Solution: 6, since √(4*9) = √36 = 6.

  17. 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

  18. More Practice • Find the geometric mean of… • 1) 7 and 63 • 2) 5 and 11 • 3) 10 and 7

  19. Homework

  20. 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?

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