Definition:Symmetry Group of Isosceles Triangle

Group Example

Let $\triangle ABC$ be an isosceles triangle whose apex is $A$.

The symmetry mappings of $\triangle ABC$ are:

the identity mapping $e$

the reflection $d$ in the line through $A$ and the midpoint of $BC$.

This group is known as the symmetry group of the isosceles triangle.

Cayley Table

The Cayley table of the symmetry group of the isosceles triangle can be written:

$\begin{array}{c|cccccc}

 & e & d \\

\hline e & e & d \\ d & d & e \\ \end{array}$

Also see

• Symmetry Group of Isosceles Triangle is Group
• Symmetry Group of Isosceles Triangle is Symmetric Group

• Results about the symmetry group of the isosceles triangle can be found here.