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

Triangle $\triangle MNQ$ and $\triangle PQN$ are oriented in a way that a single - translation will not map one onto the other as their relative positions and orientations are not in a translational relationship.

Step2: Consider rotation

A rotation can re - orient $\triangle MNQ$ to match the general orientation of $\triangle PQN$. But after rotation, the position of $\triangle MNQ$ still may not coincide with $\triangle PQN$.

Step3: Consider translation after rotation

After rotating $\triangle MNQ$ to match the orientation of $\triangle PQN$, a translation can move $\triangle MNQ$ so that it coincides with $\triangle PQN$.

Step4: Analyze reflection

There is no single line of reflection that can map $\triangle MNQ$ onto $\triangle PQN$ as their parts are not symmetrically related in a reflective sense.

Answer:

rotation, then translation