Question

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

Explanation:

Step1: Check side - length ratios

For $\triangle BCD$, sides are $5$ in, $12$ in, and $13$ in. For $\triangle WXY$, sides are $7$ in, $16.8$ in, and $18.2$ in. Calculate the ratios of corresponding sides: $\frac{7}{5}=1.4$, $\frac{16.8}{12} = 1.4$, $\frac{18.2}{13}=1.4$. The triangles are similar.

Step2: Recall congruence and rigid - motions

Rigid motions (translations, rotations, reflections) preserve side - lengths. Since the side - lengths of $\triangle BCD$ and $\triangle WXY$ are not equal (they are in a ratio of $1.4$), it is not possible to map $\triangle BCD$ onto $\triangle WXY$ using only rigid motions.

Answer:

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