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 translation

Translation moves a figure without rotating or reflecting it. Since the orientation of $\triangle MNQ$ and $\triangle PQN$ is different, translation alone won't map one onto the other.

Step2: Analyze reflection

Reflection flips a figure over a line. Just reflection won't align $\triangle MNQ$ with $\triangle PQN$ due to their relative orientations.

Step3: Analyze rotation - then - reflection

A rotation can change the orientation of $\triangle MNQ$ and then a reflection can flip it to match the position of $\triangle PQN$. This combination can map one triangle onto the other.

Step4: Analyze rotation - then - translation

Translation after rotation won't correct for the flip - like change needed to map $\triangle MNQ$ onto $\triangle PQN$.

Answer:

rotation, then reflection