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Section 8-1 Pages 432-438 Geometric Mean After today’s lesson you should be able to: - Find the geometric mean between two numbers. - Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse. Geometric Mean- for two positive numbers a and b, the geometric mean is the positive number x where the proportion a : x = x : b. This proportion can be written using fractions as a/x = x/b or with cross products x2 = ab or x = √ab. Ex. 1: Find the geometric mean between 2√2 and 3√2. 5 5 Ex. 2: The geometric mean is √24. Find b if a = 2. Theorem 8.1: ΔXYZ ~ ΔXWY Z W X Y Theorem 8.2: Z YW is the geometric mean of XW and ZW. W X Y Theorem 8.3: XZ = XY and XZ = YZ XY XW YZ WZ Z W X Y Ex. 3: Find x, y, and z to the nearest tenth. y x z 1 8 Ex. 4: Find x, y, and z to the nearest tenth. z x y 2 6