Question

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

Explanation:

To map \( \triangle MNQ \) onto \( \triangle PQN \), we analyze the transformations:

• Translation: Cannot map them as their orientations suggest more than sliding.
• Reflection only: Doesn’t align the triangles properly here.
• Rotation, then reflection: Rotating \( \triangle MNQ \) around a point (e.g., \( N \) or \( Q \)) and then reflecting aligns the congruent triangles (SSS/HL congruence supports this, as the right angles and side lengths match after rotation + reflection).
• Rotation, then translation: Unnecessary, as reflection after rotation suffices.

Answer:

C. rotation, then reflection