Segments On Hypotenuse

PROPOSITION: The hypotenuses of two dissimilar right triangles “A” and “B”, are twice the legs of a known right triangle “C”, and the altitude to hypotenuses in each of A and B triangles are identical to that in C.

HYPOTHESIS: The sum of the greater segments on each of the hypotenuses of A and B, caused by the altitude to hypotenuse in C, will equal the Perimeter of C.

For instance, triangle C can be any right triangle whose 3 sides are known.

Let “m” and “n” be the long and short legs, respectively, of C.

Let "d" be the altitude to hypotenuse of C.