Let $\triangle ABC$ be a triangle. Let $g\in\mathcal{G}$ be a line. Then Pasch Axiom states that one of the following statements holds: $g$ contains one vertex.
$g$ passes the triangle without intersecting it
$g$ intersects the triangle in exactly 2 points.
My question is: What if one side of the triangle is a segment of $g$, e.g. $\overline{AB}\in g$. Then there are infinite intersection points between $g$ and $\overline{AB}$. Is that a contradiction to Pasch's Axiom?
Some sites tell me that Pasch's Axiom is only the third statement but I've learned it this way. I can't wrap my head around it and would appreciate any help.