Describe how to draw the geometric mean in a right triangle

The height of the altitude from the hypotenuse to the vertex of the right angle is the geometric mean of the two segments formed on the hypotenuse.

The geometric mean of two numbers is the square root of the product of the numbers.

When you draw your altitude, you will divide the hypotenuse into 2 segments. The geometric mean of those two lengthsis also the height of the altitude.