Answer
$H$
Work Step by Step
Option F is incorrect. $\angle 1$ and $\angle 8$ are supplementary, not congruent.
Option G is incorrect. Vertical angles are congruent, but they do not prove that lines are parallel.
Option I is incorrect. $\angle 3$ and $\angle 5$ are same-side interior angles, which are supplementary, not congruent.
Option H is correct. $\angle 3$ and $\angle 4$ are alternate interior angles, which are congruent. If alternate interior angles are congruent, then the lines are parallel.