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:

To determine the rigid transformations mapping \( \triangle ABC \) to \( \triangle DEC \), we analyze the positions:

1. Reflection: First, reflect \( \triangle ABC \) over a vertical line (e.g., through \( C \)) to align \( BC \) with \( EC \) (since \( BC = EC \), as triangles are congruent by SSS).
2. Rotation: After reflection, rotate the reflected triangle around point \( C \) to match the orientation of \( \triangle DEC \).

Translation is not needed (no parallel shift), and dilation is not rigid (changes size, but triangles are congruent, so rigid transformations only). Rotation then translation or reflection then translation don’t fit. Reflection then rotation aligns the triangles.

Answer:

A. reflection, then rotation