New dissections to the special relationships of triangles
Extended solution (y > 2x) for 6-piece dissections of triangles with x² + y² + z² = w² ; x + y = w
w = x + y
Hingeable solution for 6-piece dissections of triangles with x² + y² + z² = w² ; x + y = w ; (compare solution 5.3, page 279 in Dissections Plane & Fancy ). I chose this solution because it is cyclicly hinged, but there are at least two other hingeable solutions existing that both use a T-strip in order to transform a parallelogram to a triangle.
w = x + y
Hingeable 6-piece dissection of triangles with x² + y² + z² = w² ; w + x = y + z ; x < y < z (compare figure 5.13, page 46 in Dissections Plane & Fancy, which requires one piece less, but is unhingeable)
w + x = y + z