Pasch's Axiom

Pasch’s Axiom is a fundamental principle in geometry that states: if a straight line crosses one side of a triangle but does not pass through any of its vertices, then it will intersect exactly one or two other sides of the triangle. In other words, a line hitting one side of a triangle inside the plane will "cut across" the figure in a predictable way, ensuring the intersections happen in a consistent manner. This axiom helps establish the logical structure of geometry, particularly in understanding how lines and triangles relate to each other.