Another Disection Proof

Loomis 18

Part II, Proof 18, page 111 from E.S.Loomis, The Pythagorean Proposition (1940)

The base square(in cyan) and riser square(in silver) are disected into three and four parts respectively. These parts exactly match (and are ready to replace) the seven parts in the hypotenuse square(dark blue.)	The exchange of parts between the hypotenuse (now silver & cyan), and the riser & base squares (now dark blue) is completed, demonstrating this elaborate disection proof.

The series of six small pictures below show the step by step exchange of parts
between the hypotenuse square (dark blue) and the base and riser squares (silver & cyan.)
[Red squares sit under the others to show displacement]

The exchanging occurs only between congruent parts. The (cyan) polygon is sliding up as the (dark blue) one slides down	Next a (silver) and a (blue) triangle are exchanged between the riser and the hypotenuse squares.	Two triangles (from the top of the base square and from the bottom of the hypotenuse square) are exchanged.
Here two small triangles are exchanged between the riser and the hypotenuse squares.	Two four-sided polygons exchange places between the riser and the hypotenuse square.	Two large trianlges exchange places, leaving only two small triangles to be moved between the riser and the hypotenuse squares.