Determining Congruence

The quadrilaterals have different orientation and location. In $ABCD,$ vertex $C$ is the bottom right vertex. In $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime },$ the corresponding vertex $C^{\prime },$ is the top left vertex. To line up their orientations, we can rotate $ABCD$ about the origin $180^{\circ }.$

Therefore, by only one transformation, we can map $ABCD$ onto $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }.$ $$\begin{array}{rl}\text{Rotation: }& 180^{\circ }\text{ rotation about the origin}\end{array}$$