In this post we are going to talk about an important concept for plane geometry, which are concepts of lines, line segments, semi-lines, among others. Line segment Definition (Line segment): given two distinct points, the union of the set of these two points with the set of points that are between them, is a line segment. In symbolic terms we have the sets: $$\overline{AB} = \\{A,B\\}\cup \\{\text{for all } X \text{ between } A \text{ and } B\\}$$Consecutive segments Definition (Consecutive Segments): two line segments are consecutive if and only if one endpoint of one of them is also the endpoint of the other.