The triangle is logical, here is why... the final shapes are not triangles.
A: the original shape is slightly concave. B: the rearranged shape is slightly convex. C: Shape A over Shape B notice that the edge is different. D: Shape B minus Shape A gives us a slice that has the same area as the missing square.
I made it... when I first looked at it, it blew my conception of reality. I figured there had to be some trick to it so I modeled the shapes in a 3D application and it was instantly apparent. I figured since I went that far I may as well render out a few images and post them.
Which way does this window face. Are the people on the inside looking to the left or looking to the right? Are you looking up into the window, or are you looking down into the window