m is the mid - point of ad. what single transformation is required to map one of these congruent triangles…

Brief Explanations:

A reflection flips a figure over a line. Given the congruent triangles $\triangle ABM$ and $\triangle DCM$ with $M$ as the mid - point of $AD$, a line can be drawn through $M$ such that one triangle can be flipped (reflected) over it to map onto the other. Rotation turns a figure around a point, translation slides a figure, and dilation changes the size of a figure. None of these would map one of these congruent triangles onto the other as effectively as a reflection in this case.

Answer:

Reflection