The statement that justifies that ∠A is congruent to ∠C is: "If two corresponding angles are congruent, then the lines that have been cut by a transversal are parallel."
When two parallel lines are intersected by a transversal, corresponding angles are congruent. In this case, ∠A and ∠C are corresponding angles as they lie on the same side of the transversal and on different parallel lines (Lines 1 and 2). The Corresponding Angles Postulate states that if a transversal intersects two parallel lines, then each pair of corresponding angles is congruent.
The other options do not directly address the relationship between corresponding angles and parallel lines:
The statement about alternate interior angles refers to the Alternate Interior Angles Theorem, which is not applicable in this context.
The statement about corresponding angles and parallel lines directly addresses the situation described, making it the correct choice.
The statement about alternate interior angles is not accurate; the correct theorem for alternate interior angles and parallel lines is not mentioned.