Final answer:
Without a diagram or additional information, it is not possible to confidently determine the missing reason in the geometric proof. Common theorems involving angles and parallel lines suggest possible answers but cannot be confirmed.
Step-by-step explanation:
The question provided asks for the missing reason in a geometric proof involving parallel lines and angles. The proof is incomplete and lacks specific details, but based on common geometric principles, we can infer possible reasons. Given that lines a and b are parallel and angle 2 is congruent to angle 3, one would typically look at geometric theorems that involve parallel lines and angle relationships, such as the Alternate Interior Angles Theorem, Corresponding Angles Postulate, or others.
Based on the options provided (A: Vertical angles are congruent, B: Alternate Interior Angles Theorem, C: Corresponding Angles Postulate, D: Consecutive Interior Angles Theorem) and the common knowledge that when a transversal crosses parallel lines, several angles are congruent or supplementary depending on their positions, the correct answer should involve these angles. However, due to the lack of a detailed diagram or additional information, we cannot provide the correct answer with full confidence. More information or a visual representation would be necessary to accurately determine the missing reason in the proof.