Question

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

Explanation:

• A translation moves a figure without rotating or flipping it. Here, just translation won't map \(\triangle MNQ\) onto \(\triangle PQN\) as their orientations are different.
• A reflection flips a figure over a line. If we consider the line \(QN\), reflecting \(\triangle MNQ\) over the line \(QN\) (after proper rotation - we can think of rotating \(\triangle MNQ\) so that the sides align in a way that reflection over \(QN\) makes sense. But in essence, the key is that reflection (after a rotation - which can be considered as part of re - orienting the figure for the reflection) can map \(\triangle MNQ\) onto \(\triangle PQN\). Rotation then translation won't work as translation doesn't flip the figure in the required way.

Answer:

reflection only