Brides Chair Proof

Loomis 15

Part II, Proof 15, page 109 from E.S.Loomis, The Pythagorean Proposition (1940)

This re-drawn Loomis figure 116 displays the disection of the base square (below the red right-triangle)
into five dis-similar parts and the riser square (to the left of the same right-triangle) into two parts.
The four images below show the translation of these parts into the (dark blue)
hypotenuse square, thus demonstrating their equal area.

The first translation is of a small (orange) square from the base square (at the bottom) into the center of the hypotenuse square (dark blue at the top.)	Next, two more shapes are moved from the base square, and attached to the left side of the riser square, thus creating four congruent triangles in the base and riser squares.	The blue triangles have been moved into the hypotenuse square, one triangle from the base and one from the riser squares.	Finally, to complete the translation into the hypotenuse square, the remianing yellow triangles are moved into place.