Any isometry that reverses the orientation of a triangle is called an [i]opposite isometry[/i].  When you read off the vertices of triangle ABC in cyclic order, they are read in a counterclockwise direction. When you read off the vertices of triangle A'B'C' in cyclic order, they are read in a clockwise direction.

[math]\sigma_m[/math] is the notation we will use for a reflection in line [i]m[/i].  [br]In the sketch below, we would write [math]\sigma_{DE}\left(A\right)=A'[/math].