Final Answer:
Given; 2. Definition of Midpoint; 3. Transitive Property justifying the congruence between segments, and then utilizes the transitive property to connect the equality between the segments, ultimately proving AB = CD. The coherence of the steps ensures a clear and valid deduction.
Explanation:
The proof relies on the given information that B is the midpoint of segment AC and C is the midpoint of segment BD. By the definition of a midpoint, it's known that when a point is the midpoint of a segment, it divides the segment into two congruent parts. Hence, the reason "Definition of Midpoint" supports the assertion that AB = BC and BC = CD.
Furthermore, using the transitive property, which states that if two quantities are equal to the same quantity, then they are equal to each other, we conclude that AB = BC = CD. Therefore, combining the given information about the midpoints and applying the transitive property establishes the equality between AB and CD, resulting in the proof of AB = CD. This logical progression satisfies the requirements of the proof provided.
This sequence of reasoning starts from the definition of a midpoint, justifying the congruence between segments, and then utilizes the transitive property to connect the equality between the segments, ultimately proving AB = CD. The coherence of the steps ensures a clear and valid deduction.