Determining Congruence

Looking at the graph, we can see that $△ABC$ and $△DEF$ have the same shape and size. What separates them are their position and orientation on the coordinate plane. Therefore, they are congruent.

In $△ABC,$ vertex $B$ is above $A$ and $C.$ In $△DEF$ the corresponding vertex, $F,$ is below $D$ and $E.$ To line up their orientations, we can rotate $△ABC$ about the origin $180^{\circ }.$ For simplicity, and since it is not congruent to any triangle, we will not draw $△GHI.$

Next, by translating $△A^{\prime }{B}^{\prime }{C}^{\prime }$ up $2$ units and right $2$ units, we can map it onto $△DEF.$

Therefore, the congruence transformation that maps $△ABC$ onto $△DEF$ is a rotation $180^{\circ }$ about the origin, followed by a translation up $2$ units and right $2$ units. $$\begin{array}{rl}\text{Rotation: }& 180^{\circ }\text{ about the origin}\\ \text{Translation: }& (x,y)\to (x+2,y+2)\end{array}$$