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Bellringer

Bellringer. Bellringer. Simplify the radical. Geometric Mean. 7-1. 7-1 Geometric Mean. Objectives Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. Geometric Mean.

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Bellringer

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  1. Bellringer

  2. Bellringer Simplify the radical.

  3. Geometric Mean 7-1

  4. 7-1 Geometric Mean • Objectives • Find the geometric mean between two numbers • Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse.

  5. Geometric Mean • The geometric mean between two numbers is the positive square root of their product.

  6. Work It • Example 1 Geometric Mean • Find the geometric mean between each pair of numbers. • 9 and 12

  7. Theorem 7.1 • If the altitude is drawn from the vertex of the right triangle to its hypotenuse then the two triangles formed are similar to the given triangle and each other. • ∆ABC ~ ∆ADB ~ ∆BDC

  8. Theorem 7.2 • The measure of an altitude drawn from the vertex of a right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse. • BD is the geometric mean of AD and CD

  9. Work it • Altitude and Segments of the Hypotenuse • In Triangle ABC, AD = 4 and CD = 12. Find BD.

  10. Theorem 7.3 • If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse then the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg. AC/BC = BC/CD AC/AB = AB/AD

  11. Bellringer • Find the geometric mean. • 10 and 20 Solve for x

  12. Hypotenuse and Segment of Hypotenuse • Find x and y in ABC.

  13. Work it • ARCHITECTURE To find the height of her school building, Mieko held a book near her eye so that the top and bottom of the building were in line with the edges of the cover. If Meiko's eye level is 5 feet above the ground and she is standing about 10.25 feet from the building, how tall is the building? Round to the nearest tenth.

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