Question

which rigid transformation would map △aec 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: Understand rigid transformations

Rigid transformations (rotations, reflections) preserve shape and size.

Step2: Analyze rotation about point \(B\)

A rotation about point \(B\) would not map \(\triangle AEC\) to \(\triangle EDC\) as the relative positions of vertices with respect to \(B\) are not consistent for such a rotation.

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

A reflection across \(\overline{AC}\) would not map \(\triangle AEC\) to \(\triangle EDC\) because the symmetry axis \(\overline{AC}\) does not align the two triangles in the required way.

Step4: Analyze rotation about point \(C\)

A rotation about point \(C\) would not map \(\triangle AEC\) to \(\triangle EDC\) as the angles and side - side correspondences do not match for a rotation about \(C\).

Step5: Analyze reflection across \(\overline{CB}\)

A reflection across the line containing \(\overline{CB}\): If we consider the line \(\overline{CB}\) as the axis of reflection, for any point \(P\) in \(\triangle AEC\), its image \(P'\) in \(\triangle EDC\) satisfies the property of reflection (distance from \(P\) to \(\overline{CB}\) is equal to the distance from \(P'\) to \(\overline{CB}\), and the line segment joining \(P\) and \(P'\) is perpendicular to \(\overline{CB}\)). So, a reflection across the line containing \(\overline{CB}\) maps \(\triangle AEC\) to \(\triangle EDC\).

Answer:

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