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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
 
 

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