True or False?
Every polygon with an even number of vertices may be partitioned by diagonals into quadrilaterals.
Any orthogonal polygon may be partitioned by diagonals into convex quadrilaterals. (The proof is available on chapter 2 of "Art Gallery Theorems and Algorithms", by Joseph O'Rourke).
We also know that orthogonal polygons have even number of vertices.
So, it's natural to guess that all polygons having an even number of vertices can be partitioned by their diagonals into quadrilaterals. Is this guess true?
Note: I already know that making the guess stronger by changing from "quadrilaterals" to "convex quadrilaterals" is not true and I have a counterexample for that. But all of the polygons I draw could be partitioned into quadrilaterals. So, if the guess is true, one should probably propose an algorithm to do the partitioning, and if not, a counterexample should be provided.