If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?
Yes.
Step 1: A ray starts at one point and goes forever in one direction.
Step 2: If two rays intersect, they share the same starting point.
Step 3: By definition, two rays with a common starting point form an angle.
Step 4: The common starting point is called the vertex of that angle.
Using simple symbols:
Let the rays be \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\).
They meet at the point \(O\).
So the angle formed is \(\angle AOB\).
The vertex of \(\angle AOB\) is \(O\).
Conclusion: Yes. The intersection point is the vertex of the angle formed by the two rays.