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.
Let "h" be the hypotenuse of C.
Then, the hypotenuses of A and B will equal 2(m) and 2(n), respectively, and the altitude to their hypotenuses will be "d", same as that in C.
Correlation: Two right triangles A and B, with hypotenuses equal to twice the legs of a known right triangle C, and the same altitude to the hypotenuse as in C, will contain acute ∠’s equal to one half the acute ∠’s in C.
The lesser acute ∠ in the triangle with the greater hypotenuse (2m), for triangle A, will be 1/2 the smaller acute ∠ in C.
The lesser acute ∠ in the triangle with the smaller hypotenuse (2n), for triangle B, will be 1/2 the greater acute ∠ in C.