The Concept of Symmetry of Figures
Big Idea: Symmetry is one of the most fundamental concepts in mathematics and nature. A figure has symmetry when it can be transformed (reflected, rotated, or translated) and still look exactly the same as the original.
1. What is Symmetry?
A geometric figure has symmetry if there exists a transformation that maps the figure onto itself. In other words, after the transformation, the figure is indistinguishable from its original position.
Formal Definition: A figure $F$ is said to be symmetric with respect to a transformation $T$ if $T(F) = F$.