Similar Triangles in Tiling a Plane When tiling the infinite plane with triangles, is it necessary for two of the triangles to be similar?
I've tried different methods to construct, but none work. My idea was to use right triangles to show that it's not necessary, but it doesn't work. 

Hint Tile the plane with squares (or rectangles).
Then for each square pick a point inside. Connect it to the four vertices. Show that you can pick the points in such a way that the triangles are not similar...
