Final answer:
The angle pairs that are not congruent when a transversal intersects parallel lines are the same-side interior angles. They are supplementary, adding up to 180 degrees, and are therefore not congruent.
Step-by-step explanation:
When a transversal intersects a pair of parallel lines, the angle pairs that will NOT be congruent are the same-side interior angles (Option C). Alternate interior angles, alternate exterior angles, and corresponding angles are congruent when a transversal crosses parallel lines. Same-side interior angles, on the other hand, are supplementary, meaning they add up to 180 degrees, but they are not necessarily congruent unless each is 90 degrees.