Definition:Symmetry Group of Line Segment

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Group Example

Let $AB$ be a line segment.


The symmetry mappings of $AB$ are:

The identity mapping $e$
The rotation $r$ of $180 \degrees$ about the midpoint 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:

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

Also see