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Harrison began a proof. ce=df because segment ce≅ segment df . cd de=ce and de ef=df , by the segment addition postulate. de ef=ce by substituting ce for df . what is a possible next step in harrison's proof?

User SeanR
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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.

User Haynar
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