Question

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

Explanation:

Step1: Recall definition of rigid - motions

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures.

Step2: Compare side - lengths of the two triangles

In $\triangle ABC$, side - lengths are $AB = 12$ mm, $AC=30$ mm, $BC = 30$ mm. In $\triangle DEF$, side - lengths are $DE = 8$ mm, $DF = 20$ mm, $EF = 20$ mm. Since the side - lengths of $\triangle ABC$ and $\triangle DEF$ are not equal ($12
eq8$, $30
eq20$), we cannot map $\triangle ABC$ onto $\triangle DEF$ using only rigid motions.

Answer:

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