Höhensatz - geometric mean
The geometric mean - Höhensatz
The geometric mean is a theorem related to Pythagoras' theorem and states that the square (hh) and the rectangle (pq) have the same area.
One proof
Proof
The two small triangles at the top right and at the bottom left are congruent (i.e., the sides are the same lengths). The rectangle which is p time q where p and q are the two legs of the small triangles has the same are as the square with sides h.