Prove: Every ray is convex.

Here is what I think:

Proof:

Let's say we have a union of a triangle and the set of all points that lie inside that triangle called A. If we place the points P,Q in there, then A becomes convex since the entire segment PQ lies in A. And since it is known that eveery segemnt PQ is a convex set, and that a set with only one point is convex, then a ray, say ray AB, ic convex also because it contains two points so it has the property of having two points.

Is this right? If it isn't, can someone please help me with it? I really do not understand how else to prove it.

Thank you for your time and effort! I really appreciate it!