Determining Congruence

In $△ABC,$ vertex $A$ is above $B$ and $C.$ In $△A^{\prime }{B}^{\prime }{C}^{\prime }$ the corresponding vertex, $A^{\prime },$ is below $B^{\prime }$ and $C^{\prime }.$ To line up their orientations, we can rotate $△ABC$ $180^{\circ }$ about the origin.

Therefore, the congruence transformation that maps $△ABC$ onto $△A^{\prime }{B}^{\prime }{C}^{\prime }$ can be written as shown below. $$\begin{array}{c}\underline{\text{Rotation}}\\ 180^{\circ }\text{ about the origin}\end{array}$$