Question

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

Explanation:

1. Recall rigid transformations: reflection, rotation, translation (dilation is non - rigid as it changes size).
2. Analyze the triangles: First, reflect $\triangle ABC$ over an appropriate line to align the sides, then rotate to match the orientation of $\triangle DEC$. Translation would move without rotation - matching, rotation then translation doesn't fit the alignment, and dilation is invalid. So reflection then rotation works.

Answer:

A. reflection, then rotation