Cover a polygon with polygons Besides right angled triangles, is there any polygon I could use to cover any given (regular or not) polygon? It's clear that given a triangle, square, hexagon or rectangle you would other options. Can this be proven, if right? That is, that the right angled triangle is the only polygon able to $100\%$ cover any other polygon.
You'll want to look at Laczkovich, M. "Tilings of Polygons with Similar Triangles." Combinatorica 10, 281-306, 1990.  

46 triangles of type $45^\circ-60^\circ-75^\circ$ can perfectly cover a square.
In FEA (Finite Element Analysis), meshing (specially triangle meshing) is required to perform the analysis.

Perhaps some insights of your proof can be found in Wikipedia, Types of Mesh: https://en.wikipedia.org/wiki/Types_of_mesh