Question

is △klm congruent to △qrs? justify your answer using rigid motions. yes. a translation and a reflection can map △klm onto △qrs. yes. a translation and a rotation can map △klm onto △qrs. no. it is not possible to map △klm onto △qrs using only rigid motions.

Explanation:

Step1: Analyze side - lengths

Both triangles have side - lengths 3 m, 6 m, 6 m, so they are congruent by SSS (Side - Side - Side) criterion. Rigid motions preserve side - lengths and angles.

Step2: Consider possible rigid motions

We can first translate one triangle so that one of its vertices coincides with the corresponding vertex of the other triangle. Then, we can perform a rotation to align the remaining sides. A translation and a rotation can map $\triangle KLM$ onto $\triangle QRS$.

Answer:

Yes. A translation and a rotation can map $\triangle KLM$ onto $\triangle QRS$.