Symmetry, as we have stated, involves a transformation of a system that leaves it looking the same as it did before. As the figure below illustrates (Fig. 9 ), an isosceles triangle has a symmetry of reflection about one of its altitudes.
Symmetries are closely related to the concept of invariances. This term, which can be used almost interchangeably with symmetries, refers to performing some operation that leaves the original object or configuration untouched or invariant.
