1. 8.2 Problem Solving in Geometry with Proportions

2. Additional Properties of Proportions 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 C E B D x 10 16 30 AB = AC 16 = 20* BD CE X 10 160 = 20X 8 = X Find the length of AC by Subtracting 10 from 20.

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

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, 15 2 = 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