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

Triangles $\triangle PQR$ and $\triangle STU$ have different orientations. A translation only moves a figure without changing its orientation, so it's not just translation.

Step2: Consider rotation

A rotation can change the orientation of a figure. But looking at the triangles, rotation alone won't map one onto the other as the orientation - related to the order of vertices - is still not correct.

Step3: Analyze reflection and translation

A reflection can change the orientation (flip the figure) and then a translation can move the reflected figure to the correct position. This combination can map $\triangle PQR$ onto $\triangle STU$.

Answer:

reflection, then translation