Prove that any n-gon can be cut into triangles by non-intersecting diagonals
Prove that the number of triangles obtained by cutting an n-gon by non-intersecting diagonals is equal to n-2
Accept induction. Pick a vertex P so that it has an adjacent vertex Q is such that PR is contained in the polygonal where R is adjacent to Q. (This is always possible). Now We have a smaller n-1 gon, which by induction is possible. Together with this triangle we have that it is always possible to "triangulate" any polygon.