Question

the triangles are congruent by the sss congruence theorem.
which rigid transformation(s) can map △abc onto △ fed?
○ reflection, then dilation
○ reflection, then translation
○ rotation, then translation
○ rotation, then reflection

Explanation:

First, note that rigid transformations preserve size and shape (dilation is not rigid, so eliminate the first option). Observe the orientation of $\triangle ABC$ and $\triangle FED$: the right angle in $\triangle ABC$ is at vertex $B$, while in $\triangle FED$ it is at vertex $E$. A reflection will flip the triangle to match the orientation of the corresponding sides, and then a translation will move the reflected triangle to overlap exactly with $\triangle FED$. Rotation alone cannot fix the flipped orientation of the sides relative to each other.

Answer:

reflection, then translation