In Euclidean geometry, if they are coplanar they must intersect. But if they are in different planes, they may not. The following example will illustrate this:
Picture yourself in a cuboid room - ie a normal shaped room. Stand with your back to one of the walls. Ray 1 forms the join of the wall behind you and the floor. Ray 2 is the line where the wall facing you meets one of the side walls. Rays 1 and 2 are not parallel but they can never meet - because they are not in the same plane.
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If rays, parallel ones. If segments there are many more options because you can have a segment that is not long enough to reach the point of intersection.
parallel lines never intersect.
no they are parallel therefore they will never intersect
If lines intersect they CANNOT BE PARALLEL. Speak to your teacher!
Lines that never intersect are parallel.