Axiom:Pasch's Axiom

Axiom

Pasch's Axiom in Euclidean Geometry

Let a triangle and a straight line lie in the same plane such that the line does not go through any of the vertices of the triangle.

Then if the line intersects one side of the triangle, it intersects another.

That is, such a straight line intersects two of the triangle's sides or none.

Pasch's Axiom in Tarski's Geometry

$\forall a, b, c, p, q: \exists x :\mathsf B a p c \land \mathsf B b q c \implies \mathsf B p x b \land \mathsf B q x a$

where $a, b, c, p, q, x$ are points.