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: Recall congruence by rigid - motions

Rigid motions (translations, rotations, reflections) preserve side - lengths and angles. For two triangles to be congruent by rigid motions, their corresponding side - lengths must be equal.

Step2: Compare side - lengths

In \(\triangle KLM\), the side - lengths are \(KL = 10\mathrm{cm}\), \(LM=6\mathrm{cm}\), \(KM = 11\mathrm{cm}\). In \(\triangle QRS\), the side - lengths are \(QR = 10\mathrm{cm}\), \(RS = 15\mathrm{cm}\), \(QS=12\mathrm{cm}\). Since the side - lengths of \(\triangle KLM\) and \(\triangle QRS\) are not equal (\(LM
eq RS\), \(KM
eq QS\)), we cannot map \(\triangle KLM\) onto \(\triangle QRS\) using rigid motions.

Answer:

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