Is it true that if two lines are crossed by a transversal the two lines are parallel?

A transversal is simply any line that passes through two or more coplanar lines each at different points. So picture, if you will, two lines that are clearly not parallel. I can easily construct a transversal that passes through them. HOWEVER, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

This is called the transversal postulate.

If the corresponding angles are congruent, than the lines are parallel. This is the converse of the first postulate.

So, the answer to your question is NO, unless the corresponding angles are congruent.