How the Altitude Divides the Hypotenuse

show expression(s) for:

legs	hypotenuse

AD

≈

0.92

AC

≈

1.56

DC

≈

0.64

AB

≈

1.20

AC×AD

≈

1.20

BC

≈

1

AC×DC

≈

1.00

Draw the altitude to the hypotenuse of a right triangle. Then each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg:

AB=

AC×AD

and

BC=

AC×DC

. Also, the length of the altitude is the geometric mean of the two segments:

BD=

AD×DC

.

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