Question

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

Explanation:

Step1: Analyze orientation

The orientation of $\triangle LMN$ and $\triangle L'M'N'$ is different. A translation only moves the figure without changing its orientation, so it cannot map $\triangle LMN$ onto $\triangle L'M'N'$.

Step2: Consider reflection

A reflection can change the orientation of a figure. After reflection, the orientation of $\triangle LMN$ can be made the same as $\triangle L'M'N'$.

Step3: Consider translation after reflection

After reflection to match the orientation, a translation can be used to move the reflected $\triangle LMN$ to the exact position of $\triangle L'M'N'$.

Answer:

reflection then translation