Two coplanar lines are cut by a transversal. Which condition does NOT guarantee that the two lines are parallel?

The condition that does NOT guarantee that the two lines are parallel is: "The corresponding angles are supplementary."

Here's why:

1. When two coplanar lines are cut by a transversal, several pairs of angles are formed.

2. If the corresponding angles (angles in the same relative position at each intersection) are congruent (equal in measure), then the lines are parallel. This is because corresponding angles are congruent when the lines are parallel.

3. If the alternate interior angles (angles on opposite sides of the transversal and inside the two lines) are congruent, then the lines are parallel. This is because alternate interior angles are congruent when the lines are parallel.

4. If the alternate exterior angles (angles on opposite sides of the transversal and outside the two lines) are congruent, then the lines are parallel. This is because alternate exterior angles are congruent when the lines are parallel.

5. If the consecutive interior angles (angles on the same side of the transversal and inside the two lines) are supplementary (add up to 180 degrees), then the lines are parallel. This is because consecutive interior angles are supplementary when the lines are parallel.

6. However, if the corresponding angles are supplementary, this does NOT guarantee that the lines are parallel. In fact, if the corresponding angles are supplementary, it suggests that the lines are likely not parallel, because corresponding angles are congruent (not supplementary) when the lines are parallel.