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 \( \triangle ABC \) with \( \triangle EDC \) as the positions of vertices relative to B do not match for such a rotation.

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

A reflection across \( \overline{CB} \) would not map \( \triangle ABC \) to \( \triangle EDC \) because the orientation and position of points A and E (relative to \( \overline{CB} \)) do not fit a reflection over \( \overline{CB} \).

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

A reflection across \( \overline{AC} \) would not map \( \triangle ABC \) to \( \triangle EDC \) as the relationship between the triangles (based on side - angle - side congruence \( \triangle ABC\cong\triangle EDC \) ( \( AC = EC\), \( \angle ACB=\angle ECD\), \( BC = DC\)) is not a reflection over \( \overline{AC} \)).

Step4: Analyze rotation about point C

Since \( AC = EC\), \( BC = DC\) and \( \angle ACB=\angle ECD\), a rotation about point C (where we can consider the rotation angle \( \angle ACE=\angle BCD\)) will map \( \triangle ABC \) to \( \triangle EDC \). Using the Side - Angle - Side (SAS) congruence criterion (\( \triangle ABC\cong\triangle EDC\): \(AC = EC\), \( \angle ACB=\angle ECD\), \(BC = DC\)), a rotation about point C will move point A to E and point B to D.

Answer:

a rotation about point C