To find the geometric mean between 2 numbers What you’ll learn: To find the geometric mean between 2 numbers To solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse.

Geometric Mean For 2 positive numbers a and b, the geometric mean is the positive number x where the proportion a:x=x:b is true, also written as or with cross products as The geometric mean between 2 numbers is the positive square of their product. Ex: find the geometric mean between each pair of numbers. 2 and 50 25 and 7

Theorem 7.1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the 2 triangles formed are similar to the given triangle and to each other. ADB~BDC ADB~ABC CDB~CBA A B C D

Theorem 7.2 The measure of an altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the 2 segments of the hypotenuse. b c d a e f

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. b c d a e f

Find x, y, and/or z 1. 2. 3. 4. A B C D x 2 14 y A B C D x 4 8 y A B C 17 6 x y z A B C D 20 x y 10 z

Homework p.346 14-34 even Quiz tomorrow on 7.1