The correct reason that can be used to prove that line m is parallel to line n is "If two lines are intersected by a transversal, and a pair of corresponding angles is congruent, then the two lines are parallel." The correct answer is option D.
Let's break down this reasoning step by step:
1. It is given that line m and line n are intersected by a transversal (a line that intersects two or more other lines).
2. We know that when a transversal intersects two parallel lines, certain pairs of angles are congruent.
3. In this case, we are looking at the pair of corresponding angles formed by the transversal. Corresponding angles are the angles that are in the same position on the lines on either side of the transversal.
4. The given reason states that if a pair of corresponding angles is congruent, then the two lines being intersected by the transversal are parallel.
5. This means that if we can find a pair of corresponding angles on line m and line n that are congruent, we can conclude that line m is parallel to line n.
To summarize, the reason stated in option D tells us that if we have a pair of corresponding angles that are congruent when a transversal intersects two lines, then those two lines are parallel.