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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Looking at the graph, we can see that $△ABC$ and $△A_{′}B_{′}C_{′}$ 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 $A$ is above $B$ and $C.$ In $△A_{′}B_{′}C_{′},$ the corresponding vertex, $A_{′},$ is below $B_{′}$ and $C_{′}.$ To line up their orientations, we can reflect $△ABC$ in the $x-$axis.

Next, by translating the rotation of $△ABC$ up $1$ unit and right $5$ units, we can map it onto $△A_{′}B_{′}C_{′}.$

Therefore, the congruence transformation that maps $△ABC$ to $△A_{′}B_{′}C_{′}$ is a reflection in the $x-$axis followed by a translation up $1$ unit and right $5$ units. $Reflection:Translation: in thex-axis(x,y)→(x+5,y+1) $