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The Betweenness Theorem

The Betweenness of Points Theorem is a theorem which states that: If A-B-C, then AB + BC = AC.

Definition: (Betweenness of Points)

A point is between two other points on the same line if its

Coordinate is between their coordinates. (More briefly, A-B-C if a<b<c or a>b>c.)


Theorem 1 -   The Betweenness of Points Theorem

If A-B-C, then AB + BC = AC.

Proof for case in which a<b<c


Betweenness Theorem can also be depicted by saying that If C is between A and B and on segment AB, then AC + CB = AB.
 
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