There are $n\ge3$ points in the plane.Prove that we can connect these points together by drawing the segments that connect them so that no two segment drawn intersect other than the vertices, and that the final figure will be a polygon with $n$ edges
Attemp: I think we need to have that no $3$ points are collinear.
Consider the convex hull of the $n$ points $P_1P_2\dots P_k, k\leq n$.
We first connect $P_1P_2$ and then we move the line $P_1P_2$ in the direction of the line $P_1P_k$ till it intersects another point $X$(note that it can't intersect $2$ points) and we connect $P_2X$ and then we do the same procedure for the line $P_1X$, and in the end after connecting some point with $P_k$, we connect $P_kP_1$.
Clearly the described algorithm will give a polygon with $n$ vertices where no $2$ non-adjacent edges intersect