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

$$AB\overline{AB}BA\overline{BA}$$

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.