Geometric Mean Theorem I

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
b
a
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