Question

find a sequence of rigid motions to take each vertex of triangle abc onto the corresponding vertex of triangle abc.

Explanation:

Step1: Identify a translation

Translate triangle \(ABC\) so that point \(A\) coincides with \(A'\). Let the translation vector be \(\overrightarrow{AA'}\).

Step2: Identify a rotation

After translation, rotate the triangle about point \(A'\) (which was \(A\) after translation) so that the sides and vertices match. The angle of rotation can be found by considering the angle between one of the sides (e.g., \(AB\) and \(A'B'\)) about the common - point \(A'\).

Answer:

First, translate triangle \(ABC\) by the vector \(\overrightarrow{AA'}\). Then, rotate the translated triangle about point \(A'\) by the appropriate angle to map the remaining vertices \(B\) and \(C\) to \(B'\) and \(C'\) respectively.