# Geometric Mean Theorem I - PowerPoint PPT Presentation

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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.

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Geometric Mean Theorem I

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### 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

### 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.

### 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

### 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

### Example 8

Find the value of b.

24

10

=

10

b