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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.