Question

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

Explanation:

• A translation moves a figure without rotating or reflecting it. But here, the orientation of the triangles is different (the right - angle positions are not in the same direction if we just consider translation).
• A rotation alone would not align the triangles in the correct orientation (the side - length correspondences in terms of position would not match).
• If we first reflect \(\triangle PQR\) (to get the correct orientation of the right - angle and side - length positions relative to the other triangle) and then translate it (to move it to the position of \(\triangle STU\)), we can map \(\triangle PQR\) onto \(\triangle STU\).

Answer:

reflection, then translation