Question

for problems 3 - 5, use a transparency to determine whether the given figures are congruent. if so, describe a sequence of rigid motions that maps one figure onto the other. if not, explain how you know.

1. figure abc and figure def

Explanation:

Step1: Analyze the shapes

Both figures are composed of three - point connections with an arc. Assume they are congruent.

Step2: Determine the rigid motion

First, rotate figure \(ABC\) \(180^{\circ}\) around a suitable center (for example, the mid - point of the line segment connecting \(A\) and \(D\) if we consider the orientation). Then, translate the rotated figure so that the corresponding points (e.g., \(A\) to \(D\), \(B\) to \(F\), \(C\) to \(E\)) coincide.

Answer:

Yes, the figures are congruent. A sequence of rigid motions is a rotation (e.g., \(180^{\circ}\) around an appropriate center) followed by a translation that maps \(ABC\) onto \(DEF\).