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

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- October 12th 2007, 09:45 PManncarProofs- induction in geometry
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 - October 13th 2007, 05:10 PMThePerfectHacker
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.

- October 14th 2007, 02:50 AManncar
Hi. I'm not sure i completely understand you proof. Can you please go into more detail?