Which of the following theorems cannot be used to prove two lines are
parallel?

Answer:
Option H
Step-by-step explanation:
Option F
If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.
True.
Option G
If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.
True
Option H
If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.
Since, vertical angles don't prove the lines cut by a transversal are parallel.
So the statement is False.
Option J
If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.
True.