Let $X$, $Y$ and $Z$ be three similar n-gons with the following property:
- One can glue together $X$ and $Y$ along one of the edges to get $Z$.
Examples would be rectangular triangles and also rectangles where the ratio of the sides is $\sqrt{2}$.
Already with quadrilaterals it becomes hard to fulfil the condition and it is probably worse with higher n-gons.
Are my examples the only existing ones? Can someone give and prove a list of all such n-gons?