In a right triangle, the altitude on the hypotenuse divides the altitude into two segments. The geometric mean theorem provides proportions relating the lengths of these segments of hypotenuse to the lengths of legs and the length of the altitude.

In the above diagram, triangle ABC is a right triangle right angled at C.

CD is the altitude drawn on hypotenuse AB which divides AB into two segments

AD and

DB.

In a right triangle the length of the altitude from the right angle to the hypotenuse is the geometric mean of the length of the two segments of the hypotenuse made by the altitude.

With reference to the diagram given above the statement of the above theorem can be written as

CD

^{2} = AD . BD or CD = $\sqrt{AD.BD}$

If the length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the segment of the hypotenuse adjacent to it.

Using the diagram above the above statement can be explained by the following two equations:

AC^{2} = AB . AD or AC = $\sqrt{AB.AD}$

and

BC^{2} = AB . BD or BC = $\sqrt{AB.BD}$