Given any line, there are points on the line and points not on the line.
Given two distinct points there exists a unique line passing through those points.
Given three points on a line, one and only one of them is between the other two.
Given two points $A$ and $B$ there always exists a point $C$ between $A$ and $B$ and a point $D$ such that $B$ is between $A$ and $D$.
A line $m$ determines exactly two distinct semi planes, whose intersection is the line $m$.
Pasch's axiom: If a line not going through the vertices of a triangle (here I'm excluding the degenerate case of a triangle formed by three points on the same line) intersects one side, then it intersects another side.