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

Question

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.

Answer 1

(1) Every triangle must be a subset of the convex hull. (2) Suppose some edge of the convex hull doesn't belong to any triangle -> contradiction.