Line Segments#
Definition: Line Segment
A line segment is a curve which has no Curvature and has a parametrization of the form \(\gamma: [a;b] \to \mathbb{R}^n\).
Notation
If \(A = \gamma(a)\) and \(B = \gamma(b)\), then we denote the line segment as
\[ AB \qquad \overline{AB} \qquad BA \qquad \overline{BA} \]
Extension#
Theorem: Extension of a Line Segment
For each line segment \(s\) there exists one and only one Straight Line \(l\) which contains \(l\), i.e. \(s \subset l\).
Proof
TODO
Definition: Extension of a Line Segment
The extension of a line segment is the unique Straight Line which contains it.
Midpoint#
Definition: Midpoint
The midpoint of a line segment is the point which divides it into two congruence line segments.