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Geometric Mean Theorem I Geometric Mean Theorem I Geometric Mean (Altitude) Geometric Mean (Altitude) Theorem 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 b a b x x a a b x Heartbeat Heartbeat

Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

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Page 1: Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

Geometric Mean Theorem IGeometric Mean Theorem I

Geometric Mean (Altitude) Geometric Mean (Altitude) TheoremTheorem

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

ba

b

x

x

a

a b

xx

HeartbeatHeartbeat

Page 2: Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

Geometric Mean Theorem IIGeometric Mean Theorem II

Geometric Mean (Leg) Geometric Mean (Leg) TheoremTheorem

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.

x

a

a

c

x

c

a

y

c

b y

b

b

c

Page 3: Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

Geometric Mean Theorem IIGeometric Mean Theorem II

Geometric Mean (Leg) Geometric Mean (Leg) TheoremTheorem

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.

x

a

a

c

x

c

a

y

c

b y

b

b

c

BoomerangBoomerang

c

aa

x

Page 4: Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

Geometric Mean Theorem IIGeometric Mean Theorem II

Geometric Mean (Leg) Geometric Mean (Leg) TheoremTheorem

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.

x

a

a

c

x

c

a

y

c

b y

b

b

c

BoomerangBoomerang

c

bb

y

Page 5: Geometric Mean Theorem I Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse

Example 8Example 8

Find the value of b.

2410= 10b

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