Definition:Symmetry Group of Line Segment

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Group Example

Let $\triangle AB$ be a line segment.


The various symmetry mappings of $AB$ are:

The identity mapping $e$
The rotation $r$ of $180^\circ$ about the center of $AB$.

This group is known as the symmetry group of the line segment.

Cayley Table

The Cayley table of the symmetry group of the line segment can be written:

$\begin{array}{c|cccccc} & e & r \\ \hline e & e & r \\ r & r & e \\ \end{array}$

Group Presentation

Its group presentation is: Symmetry Group of Line Segment/Group Presentation

Also see