That the rotated interior quadrilateral—the ‘square donut’—
is indeed a square is easily shown. Each interior corner
angle associated with the interior quadrilateral is part of a
three-angle group that totals
0
180 . The two acute angles
flanking the interior corner angle sum to
0
90 since these
are the two different acute angles associated with the right
triangle. Thus, simple subtraction gives the measure of any
one of the four interior corners as
0
90 . The four sides of
the quadrilateral are equal in length since they are simply
four replicates of the hypotenuse of our basic right triangle.
Therefore, the interior quadrilateral is indeed a square
generated from our basic triangle and its hypotenuse.