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:

Step1: Analyze triangle orientation

The orientation of $\triangle MNQ$ is different from $\triangle PQN$. A translation alone would not change the orientation, so translation - only is incorrect.

Step2: Consider rotation

A rotation can change the orientation of the triangle. After rotating $\triangle MNQ$ to match the general orientation of $\triangle PQN$, a reflection may be needed to precisely map one triangle onto the other.

Step3: Evaluate options

A rotation - then - translation would not correct for the possible mirror - image difference. A reflection - only may not be sufficient to align the triangles in the correct position and orientation. A rotation followed by a reflection can map $\triangle MNQ$ onto $\triangle PQN$.

Answer:

rotation, then reflection