Question

In a word processing document or on a separate piece of paper, use the guide to construct a two-column proof proving AC > EF given BC = EF. Submit the entire proof to your instructor. Given: BC = EF Prove: AC > EF
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Answer 1

Answer:

Complete proof is written below.

Facts and explanation about the segments shown in question :

1. As BC = EF is a given statement in the question
2. AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
3. AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
4. AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.

Below is the complete proof of the observation given in the question:

STATEMENT                              REASON  

___________________________________________________

1. BC = EF                                    1. Given

2. AB + BC = AC                         2. Betweenness

3. AC > BC                                   3. Def. of segment inequality

4. AC > EF                                   4. Def. of congruent segments

Keywords: statement, length, reason, proof

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