1. 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.

2. 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

3. 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

4. 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

5. 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

6. 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 C17 6 x y z A B C D 20 x y 10 z

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