Well the triangle would be divided in how many parts would depend on the fact that whether the n points chosen include the end points of third line or not ? If we assume that the end points are excluded then we can divide the triangle in n+1 parts. But how do we reach this soultion? well let us start with n = 1. Now if we join that point with the opposite vertex then we have divided the triangle in two (1 + 1) parts. Similarily if we further visualize we can see that n points will result in n+1 parts.