If three distinct points are collinear, then one of the points is between the other two. 4. Important subsets of lines are segments, half-lines and rays. A line segment consists of two points and all collinear points between them. Intersecting lines are two lines with exactly one point in common. Concurrent lines are lines that contain a single common point.
Parallel lines are lines with no points in common.
A unique line is determined by two distinct points. A unique plane is determined by three non-collinear points. This axiom can be used to prove that any of the following conditions also generates a unique plane. If the intersection of two distinct planes is not empty, then the intersection is a line. If a line contains two distinct points of a plane, then the line lies in the plane.