1. The problem statement, all variables and given/known data A triangulation of a convex polygon is a decomposition of the polygon into triangles whose interiors do not overlap and whose vertices lie at vertices of the polygon. Prove that there are Cn−2 ways to triangulate an n-sided convex polygon 2. Relevant equations cn= (1/2)(2n choose n) 3. The attempt at a solution I tried a proof by induction: let n=3. there is only one way to triangulate a triangle, and cn-2=c1=(1/2)(2 choose 1)=1. So the statement holds for n=3 now assume the statement holds for n=k So the number of ways to triangulate a k-sided polygon is Ck-2=(1/2)(2(k-2) choose k-2) Now let n=k+1 This is where I get stuck and I dont' know what to do.... any help/hints would be appreciated.