Question

the triangles are congruent by the sss congruence theorem. which transformation(s) can map δlmn onto δlmn? translation only reflection only rotation then translation reflection then translation

Explanation:

Step1: Observe orientation of triangles

The orientation of $\triangle LMN$ and $\triangle L'M'N'$ is different. A translation alone will not change the orientation, so translation - only is incorrect.

Step2: Analyze reflection

A reflection can change the orientation of a figure. But just reflection may not place the triangle in the exact position of $\triangle L'M'N'$.

Step3: Consider rotation and translation

A rotation can change the orientation and a subsequent translation can move the rotated triangle to the position of $\triangle L'M'N'$.

Step4: Consider reflection and translation

A reflection can change the orientation and a translation can move the reflected triangle to the position of $\triangle L'M'N'$.

Answer:

reflection then translation