Question

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

Explanation:

Step1: Check side - lengths for congruence

In $\triangle QRS$, the side - lengths are $QR = 15$ cm, $QS=8$ cm, $RS = 17$ cm. In $\triangle TUV$, the side - lengths are $UT = 15$ cm, $TV = 20$ cm, $UV = 25$ cm. Since the side - lengths of $\triangle QRS$ and $\triangle TUV$ are not equal ($8
eq20$, $17
eq25$), rigid motions (translations, rotations, reflections) which preserve side - lengths and angles cannot map $\triangle QRS$ onto $\triangle TUV$.

Answer:

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