Simple Geometry Proof (Betweenness Axiom)

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Homework Statement


Given a line l, a point A on l, and a point B not on l. Then every point of the ray AB (except A) lies on the same side of l as B.


Homework Equations





The Attempt at a Solution



I understand why this is true, however I'm having some trouble wording my proof. Any help would be great!

Alright, this is what I have so far:

Suppose there exists a point c on the ray AB such that c lies on the opposite side of l than B.
However, By definition of a ray, A*B*C

(this is where I don't know how to continue wording my proof, I know that since B is between a and c, and the line goes through A, that means that C must be on the same side of l as B, however I don't know how to word that mathematically)
 

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