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. First, analyze the position of \(\triangle ABC\) and \(\triangle DEC\). A reflection over an appropriate line (e.g., a line through point \(C\)) can align the orientation of \(\triangle ABC\) closer to \(\triangle DEC\).
2. After reflection, a rotation about point \(C\) (or another suitable point) can map \(\triangle ABC\) exactly onto \(\triangle DEC\).
3. Translation is not needed here as the triangles share a common vertex \(C\) (or can be aligned around \(C\) with rotation after reflection), and dilation is a non - rigid transformation (rigid transformations preserve size, so dilation is excluded). Also, rotation then translation or reflection then translation don't fit the positional relationship as well as reflection then rotation.

Answer:

A. reflection, then rotation