Final answer:
To prove that ∠3 is congruent to ∠4, theorems such as the Vertical Angle Theorem or the Alternate Interior Angles Theorem could be applied, depending on the geometrical relationships present in the figure, which is not provided in the question.
Step-by-step explanation:
Without a specific figure provided, we cannot directly address the relationships between ∠1, ∠2, ∠3, and ∠4 to use in a two-column proof. However, a two-column proof typically consists of a list of statements and reasons that explain why certain properties and theorems are used to arrive at a conclusion based on given information. To prove that ∠3 is congruent to ∠4, one must use theorems such as the Vertical Angle Theorem, which states that vertical angles are equal, or perhaps other geometric theorems like the Alternate Interior Angles Theorem if transversals and parallel lines are involved.
Without the figure, we can only hypothesize about the setup and the potential reasoning steps that would be used to approach a proof like this. If ∠1 and ∠2 are given as congruent, potential reasons for ∠3 being congruent to ∠4 might include them being alternate interior angles, corresponding angles, or vertical angles, depending on the specific layout of the geometrical figure in question.