Pythagorean theorem: Interactive puzzle

Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

You've proved
the Pythagorean theorem!
Choose another partitioning:

Theorem (Boyaj, 1832; Gervin, 1833).

If two poly­gons have the same area, then they are decom­pos­able in the same set of poly­gons.

That is, if two poly­gons have equal areas, then any of them can be decom­posed into a finite set of pieces with which it is possible to recon­struct exactly the other polygon.