Question

the triangles are congruent by sss or hl. which transformation(s) can map △mnq onto △pqn? translation only reflection only rotation, then reflection rotation, then translation

Explanation:

A reflection is a transformation that flips a figure over a line. In this case, if we consider the line \(NQ\) (or an appropriate line of symmetry), \(\triangle MNQ\) can be reflected over that line to map onto \(\triangle PQN\). A translation moves a figure without rotating or flipping it, and since the orientation (in terms of the right - angle position relative to the common side \(NQ\)) changes, translation only is not sufficient. A rotation changes the orientation of a figure around a point, and then a reflection would be an extra (unnecessary) step as a single reflection can achieve the mapping. A rotation then translation also over - complicates as the key transformation is the reflection.

Answer:

reflection only