The geometric mean is the positive square root of the product of
The geometric mean between 2 and 4 is x. The proportion 2:x=x:4
must be true hence
If we in the following triangle draw the altitude from the
vertex of the right angle then the two triangles that are formed
are similar to the triangle we had from the beginning. The two
triangles formed are also similar to each other.
The measure of the altitude drawn from the vertex of the right
angle to the hypotenuse is the geometric mean between the measures
of the two segments of the hypotenuse. Hence BD is the geometric
mean of AD and DC.
Also in our figure the measure of a leg of the triangle is the
geometric mean between the measures of the hypotenuse and the
segment of the hypotenuse adjacent to that leg.
Video lesson: Find the value of x in the