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

Answer 1

Answer:

The complete proof with diagram, statements and mathematical reasons is attached in the attached figure a.

Step-by-step explanation:

Let suppose the line segments AC and EF are shown in the attached figure a.

• From the diagram, it is clear that BC = EF as given in the question you have asked.
• It is clear that AB + BC = AC. This reason is that, in mathematics, where the length of segments and a point on that particular segment is involved, betweenness clearly states that the length of the segment AB and the segment BC would be equal to the length of the segment AC, if there lied a point between the points A and C. Segment addition postulates also states that AC would be equal to AB+BC. For example, if AB = 7 and BC = 9 then AC = AB + BC ⇒ 16
• It is clear that AC > BC because the Parts Theorem (Segments) states that the the point B lies on the segment AC between A and C, then AC would be greater than BC and AC would also be greater than AB, as shown in figure a.
• It is clear that AC would be greater than EF as BC = EF, and if AC is greater than BC, then it should also be the fact that the length of AC must have to be greater than the length of the line segment EF.

The complete proof with diagram, statements and mathematical reasons is attached in the attached figure a.

Keywords: statement, segment, reason, mathematical proof

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