Final answer:
The question involves proving that line segment DE is parallel to line segment AB, given congruent angles. The proof would use the properties of parallel lines and the Converse of the Alternate Interior Angle Theorem to show this relationship.
Step-by-step explanation:
The student's question pertains to a geometric proof involving angle congruence and parallel lines. Given that ∠CDE ≅ ∠CED and ∠A ≅ ∠B, we aim to prove that DE || AB. In a geometric proof, a common strategy is to use the concept of alternate interior angles, which states that if two angles are congruent and are on the inside of a pair of lines but on opposite sides of a transversal, then those lines are parallel. Since ∠CDE and ∠CED are congruent, DE can be considered as a transversal, which suggests that AB is parallel to DE. This logical conclusion can be further bolstered by knowing that ∠A ≅ ∠B, providing more evidence of parallel lines due to congruent alternate interior angles which align with the Converse of the Alternate Interior Angle Theorem. The proof in its entirety would involve establishing these relationships step by step, justifying each through the properties of parallel lines and angles.