Final Answer:
The correct completion of the missing statement is: m∠abc = m∠bed; Corresponding Angles Theorem.
Step-by-step explanation:
The Corresponding Angles Theorem states that when a transversal intersects two parallel lines, the corresponding angles are congruent. In this case, m∠abc and m∠bed are corresponding angles because they are on the same side of the transversal and the lines are parallel.
To understand why the Alternate Interior Angles Theorem is not applicable here, we need to consider the positioning of the angles. Alternate Interior Angles are formed when a transversal intersects two lines, and the angles are on opposite sides of the transversal and between the lines. In the given scenario, m∠abc and m∠ced are not alternate interior angles.
Therefore, the justification for the missing statement is the Corresponding Angles Theorem because m∠abc and m∠bed are corresponding angles in the context of parallel lines and a transversal.
This conclusion is based on the fundamental principles of angle relationships formed by parallel lines and a transversal. The correct application of these theorems ensures a valid and logically sound two-column proof.