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 translation

Translation moves a figure without rotating or flipping. Observing the triangles, a simple translation won't align them as their orientations are different.

Step2: Analyze reflection

Reflection flips a figure. But just reflection won't position the triangle correctly as there is a need for re - positioning in space.

Step3: Analyze rotation then translation

Rotation changes the orientation. But after rotation, the position relative to the other triangle (in terms of spatial placement) still won't match without a translation.

Step4: Analyze reflection then translation

First, reflecting $\triangle LMN$ changes its orientation to match the general orientation of $\triangle L'M'N'$. Then, translating (shifting) the reflected triangle can map it exactly onto $\triangle L'M'N'$ as required.

Answer:

reflection then translation