Final answer:
Harrison's proof involves using the Segment Addition Postulate to show congruency between segments. A potential next step would be to apply the transitive property to prove CD and EF segments are congruent.
Step-by-step explanation:
Harrison is working on a geometric proof involving segments. He has already established that segment CE is congruent to segment DF. He then uses the Segment Addition Postulate, which states that if a segment is added to two congruent segments, then the resulting segments are also congruent. Thus, if CD + DE = CE and DE + EF = DF, and CE is congruent to DF, it follows that CD + DE must also be congruent to DE + EF.
A possible next step in Harrison's proof could be to show that the segments CD and EF are congruent by transitive property, given that CD + DE = DE + EF and CE ↔ DF (implying CD + DE ↔ DE + EF). This would show that CD and EF are equal in length since they are part of equal larger segments under addition.