Perigal’s Proof and Tiling

The model explains how to derive Henry Perigal’s dissection proof of the Pythagorean theorem from the Pythagorean tiling of the plane with squares of two sizes. Restore the proof from the figure. The shape of the triangle can be changed by dragging point A. This point can take only a limited range of positions, but it suffices to cover all possible triangle shapes. Why?