Question

which rigid transformation would map △abc to △edc? a rotation about point b a reflection across the line containing cb a reflection across the line containing ac a rotation about point c

Explanation:

Step1: Analyze rotation about point B

Rotation about point B would not align the triangles as \( \triangle ABC \) and \( \triangle EDC \) have no common center of rotation at B for such a mapping.

Step2: Analyze reflection across line \( \overline{CB} \)

If we consider reflection across \( \overline{CB} \), the orientation and side - angle - side (SAS) congruence (since \( AC = EC \), \( \angle ACB=\angle ECD \), \( BC = DC \)) can be used. A reflection across the line containing \( \overline{CB} \) will map \( \triangle ABC \) to \( \triangle EDC \). The reflection swaps the positions of points A and E (with respect to the line \( CB \)) while keeping \( C \) and \( B \) (or \( D \) as \( CB = CD \)) in relevant positions.

Step3: Analyze reflection across line \( \overline{AC} \)

Reflection across \( \overline{AC} \) would not map \( \triangle ABC \) to \( \triangle EDC \) as the side - angle - side relationships and point positions do not match for this reflection.

Step4: Analyze rotation about point C

Rotation about point C: If we rotate about point C, the side - angle - side congruence ( \( AC = EC \), \( \angle ACB=\angle ECD \), \( BC = DC \)) is better achieved through reflection (which is a type of rigid transformation that can flip the triangle over the line \( CB \)) rather than rotation. Rotation about C would require a rotational angle calculation, and the visual and congruence (SAS) fit is more straightforward with reflection across \( CB \).

Answer:

a reflection across the line containing \( \overline{CB} \)