# Reflection

A reflection is, put simplify, like flipping a planar figure over a mirror. The figure has the same shape and size, except it is facing the opposite direction. When working in two dimensions, you can use a line as the "mirror". Once we reflect a figure across this line, we will find that every point is symmetric to its reflection with respect to the line. This means that, if you folded the paper over the line, the two figures would line up. Therefore, any point on the original is the same distance from the line of reflection as its reflection is.

It is also possible to have reflection about a point. This is essentially a rotation of $180^{\circ}$. To do this, suppose we have triangle $ABC$ and wish to rotate it around point $O$. Draw $OA$. Then, double its length so that it reaches point $A'$, such that $O \in$ segment $AA'$, and $OA=OA'$. Do this for the other points to get reflected triangle $A'B'C'$. $A',B',$and$C'$ are now said to be symmetric to $A,B,$ and $C$ respectively, with respect to $O$. (Pardon the pun.)