Question

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

Explanation:

Step1: Analyze orientation of triangles

The orientation of $\triangle PQR$ and $\triangle STU$ is different. A translation alone would not change the orientation, so it's not translation only.

Step2: Consider rotation

A rotation alone might not be sufficient to map one triangle onto the other considering the relative positions of vertices.

Step3: Analyze rotation - reflection combination

A rotation first would not align the triangles perfectly as the orientation issues still remain.

Step4: Analyze reflection - translation combination

A reflection can change the orientation of $\triangle PQR$ to match the orientation of $\triangle STU$, and then a translation can move it to the exact position of $\triangle STU$.

Answer:

reflection, then translation