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 translation

Translation moves a figure without rotation or reflection. Observing the orientation of \(\triangle PQR\) and \(\triangle STU\), a simple translation cannot map \(\triangle PQR\) to \(\triangle STU\) as their orientations (with respect to the right - angle) are different in terms of direction (not just position).

Step2: Analyze rotation

Rotation changes the orientation of a figure around a point. But just a rotation would not align the triangles in the correct position (since their positions relative to each other also need a shift which is not just rotational).

Step3: Analyze rotation then reflection

Rotation then reflection would change both the orientation (more than needed) and the position in a non - matching way.

Step4: Analyze reflection then translation

First, reflect \(\triangle PQR\) (this changes its orientation to match the general angular orientation of \(\triangle STU\) in terms of the right - angle direction). Then, translate the reflected \(\triangle PQR\) (move it without rotation or reflection further) to map it exactly onto \(\triangle STU\).

Answer:

reflection, then translation