Question

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

Explanation:

Step1: Check side - length ratios

$\triangle RST$ has side - lengths $1.6$ m, $2.4$ m, $3.2$ m. $\triangle IJK$ has side - lengths $2.4$ m, $3.6$ m, $4.8$ m. Calculate the ratios of corresponding sides: $\frac{1.6}{2.4}=\frac{2}{3}$, $\frac{2.4}{3.6}=\frac{2}{3}$, $\frac{3.2}{4.8}=\frac{2}{3}$. The triangles are similar.

Step2: Analyze rigid motions

Rigid motions (translations, rotations, reflections) preserve side - lengths. Since the side - lengths of $\triangle RST$ and $\triangle IJK$ are not equal (they are in a ratio of $\frac{2}{3}$), it is not possible to map $\triangle RST$ onto $\triangle IJK$ using only rigid motions.

Answer:

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