Morley's Theorem

The other way around...

Although any equilateral triangle can be obtained by the intersection of adjacent angle trisectors of an infinite number of other triangles, the same does not happen with parallelograms. In fact, given any parallelogram, there are at most two parallelograms that give rise to it (and there may even be none), as can be seen with the following applet:

(Click on the points $$A$$, $$B$$ and $$C$$ to change the shape of the parallelogram $$[ABCD]$$)