Question

e congruence: sss and hl
the triangles are congruent by sss or hl.
which transformation(s) can map \\( \triangle mnq \\) onto \\( \triangle pqn \\)?
rotation, then reflection
rotation, then translation
translation only
reflection only

Explanation:

Step1: Analyze the position of triangles

We observe the relative position of \(\triangle MNQ\) and \(\triangle PQN\). A reflection over the line \(NQ\) (the common side of the two right - angled triangles \(\triangle MNQ\) and \(\triangle PQN\)) can map one triangle onto the other.

Step2: Check other transformation combinations

• Rotation then reflection: Unnecessary as a single reflection can do the job.
• Rotation then translation: Unnecessary as the triangles are adjacent with a common side and orientation can be adjusted by reflection.
• Translation only: Translation would move the triangle without re - orienting it (since they are right - angled in opposite directions relative to the common side \(NQ\), translation alone won't work).

Answer:

reflection only