Question

the triangles are congruent by the sss congruence theorem.
which rigid transformation(s) can map $\triangle abc$ onto $\triangle dec$?
\bigcirc reflection, then rotation
\bigcirc reflection, then translation
\bigcirc rotation, then translation
\bigcirc rotation, then dilation

Explanation:

Rigid transformations preserve size and shape, so dilation (which changes size) is invalid. Observing the triangles: first reflect $\triangle ABC$ over a line through point $C$ to align the orientation, then rotate around point $C$ to map it onto $\triangle DEC$. Reflection followed by translation or rotation followed by translation would not align the shared vertex $C$ correctly.

Answer:

A. reflection, then rotation