I am taking a geometry class right now and it is pretty difficult. If you would be willing to help me with this, that would be great.

The definition of parallel is that the sum of the angles on each side of the transversal of two lines is two right angles. From this we can show that the alternate interior angles are congruent.

In our case, we have that the alternate interior angles are congruent, that is, we have that there are two pairs of alternate interior angles that are congruent, and that together one angle from each pair forms a straight angle, as you go along the lines.
This means that the sum of the angles on each side of the transversal, one from each pair, is two right angles. The lines are parallel.

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I can't draw here yet.