To prove that two lines cut by a transversal are parallel, one must show that
last time giving the wrong answer!

I think you forgot to give the options along with the question. I am answering the question based on my knowledge and research. To prove that two lines cut by a transversal are parallel, one must show that alternate interior angles are congruent, alternate exterior angles are congruent and corresponding angles are congruent. I hope the answer helped you.