[math-fun] Points and lines puzzle

I just read this puzzle and thought math-fun might enjoy it: Let N be a positive integer. Suppose that we are given 2N points in the plane such that no 3 of them are collinear. Assume N points are chartreuse and the other N are heliotrope. Prove there exists a one-to-one correspondence between the chartreuse points and the heliotrope points such that if each point is connected to its buddy by a line segment, then the N line segments are disjoint. —Dan