When can two angles said to be Parallel?

If two lines are cut by a transversal, and the corresponding angles are congruent (congruent angles have the same measure), the lines are parallel 2.if two lines are cut by a transversal, so that alternate interior angles are congruent, the lines are parallel. in the example below, line e is parallel to line f because angle 3.if two lines are cut by a transversal so that interior angles on the same side of the transversal are supplementary, the lines are parallel 4.if two lines are perpendicular to another line, and they (the two lines) are in the same plane, then they are parallel. the example problem above is a perfect example of this. be careful with this rule because it is possible to have two lines that are perpendicular to a third line that are not in the same plane