Question

is △def congruent to △xyz? justify your answer using rigid motions.
yes. a translation and a reflection can map △def onto △xyz.
yes. a translation and a rotation can map △def onto △xyz.
no. it is not possible to map △def onto △xyz 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 $\triangle DEF$, the side - lengths are $DE = 5$ cm, $DF=12$ cm, and $EF = 13$ cm. In $\triangle XYZ$, the side - lengths are $XY = 9$ cm, $XZ = 12$ cm, and $YZ=15$ cm. Since $DE
eq XY$, $EF
eq YZ$, and although $DF = XZ$, not all corresponding side - lengths are equal.

Answer:

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