1. Geometric Mean Theorem I
Heartbeat
Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments. x x a b

2. Geometric Mean Theorem II
Geometric Mean (Leg) Theorem The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

3. Geometric Mean Theorem II
Boomerang
Geometric Mean (Leg) Theorem The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. a a x c

4. Geometric Mean Theorem II
Boomerang
Geometric Mean (Leg) Theorem The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. b b y c

5. Example 8
Find the value of b. 24 10 = 10 b