# Prove that the convex hull is the union of all the triangles determined by triples of points from X

I'm trying to prove that the convex hull of a set X of three or more points in the plane is the union of all the triangles determined by triples of points from X, however I can't think of the meaningful approach to go with. And now I'm really interested what kind of theorems or rules would explain how is the convex hull a union of all the triangles determined by triples of points from X.

• If $C$ is that convex hull and $T$ is the union of those triangles, you need to prove that $C\subseteq T$ and $T\subseteq C$. Have you tried either proof? To work with this problem you need to know the rigorous definition of the convex hull of a set; do you know it? – Greg Martin Nov 4 '19 at 16:44