Question

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

Explanation:

1. First, analyze the triangles \(\triangle MNQ\) and \(\triangle PQN\). The triangles are congruent right - angled triangles.
2. A translation would not map \(\triangle MNQ\) onto \(\triangle PQN\) because the orientation and position relationship is not a simple translation. A reflection only would not work as the initial orientation of the triangles (the right - angle position and the side positions) does not allow a direct reflection to map one onto the other.
3. If we first rotate \(\triangle MNQ\) around a point (for example, around point \(Q\) or \(N\)) to align the sides in a way that is closer to the orientation of \(\triangle PQN\), and then perform a reflection over a line (such as the line \(QN\)), we can map \(\triangle MNQ\) onto \(\triangle PQN\). A rotation followed by a translation is not necessary as the final position can be achieved with a rotation and then a reflection.

Answer:

C. rotation, then reflection