Is it true that when a plane is drawn through two lines, these lines will intersect?

Answer: The statement is wrong.

First, it should be noted that this statement will be true only if both lines are located directly in this plane. If the plane simply intersects two straight lines lying in other planes, then their intersection is not necessary.

Secondly, even if both lines lie in the same plane, they will intersect only if they are not parallel to each other in this plane.

That is, this statement is partially true.