Theorem 68

From the Fifteen-Year-Old's geometry textbook, Geometry for Enjoyment and Challenge, Theorem 68:

If an altitude is drawn to the hypotenuse of a given right triangle, then (a) the two triangles formed are similar to the given right triangle and to each other; (b) the altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse; and (c) either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg (i.e., the projection of that leg on the hypotenuse).

Richard Rhoad, George Milauskas, and Robert Whipple, authors of said Geometry for Enjoyment and Challenge, I summon you all to the bar of the Hypatian Court for trial on the charge of exceeding the allowable maximum of dorky impenetrability in the teaching of geometry.