A line segment is defined as a portion (set of internal points) of a straight line between two points A and B (called extremes of the line segment). A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.
A line segment divides the straight line on which it lies into two half-lines (originating respectively from points A and B). The two half-lines are therefore called extensions of the AB line segment. Two line segments are said to be consecutive if they have only one extreme in common, while they are said to be adjacent if in addition to having an extreme in common they also belong to the same straight line of origin. Finally, a line segment is null if its ends coincide, that is, since it has no internal points, it reduces to the concept of the only point.
Properties of the line segment
- Two line segments are consecutive if they have one end in common and no other point;
- two line segments are said to be congruent if they can be superimposed so that they coincide point by point;
- two consecutive line segments are adjacent if they belong to the same straight line;
- two line segments are external if they have no points in common;
- two line segments are said to be incidents when they have a single point in common, called intersection, which is not extreme for both;
- two line segments are said to be coincident if they both have extremes in common;
- two line segments are superimposed if they have one end in common and all the points of one (the minor one) are in common with the points of the other line segment.