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 - length equality

In $\triangle KLM$, two sides are 48 ft. In $\triangle QRS$, two sides are 48 ft. But the third - side lengths are different ($KL = 35$ ft and $RQ=53$ ft).

Step2: Recall rigid - motion property

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. Since the side - lengths of the two triangles are not all equal, we cannot map one triangle onto the other using only rigid motions.

Answer:

No. It is not possible to map $\triangle KLM$ onto $\triangle QRS$ using only rigid motions.