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

, then AC + CB = AB.