Question

practice problems
1 quadrilateral abcd is congruent to quadrilateral abcd.
describe a sequence of rigid motions that takes a to a, b to b, c to c, and d to d.

Explanation:

Step1: Translate the quadrilateral

Translate quadrilateral \(ABCD\) so that point \(B\) maps to point \(B'\).

Step2: Rotate the translated quadrilateral

Rotate the translated quadrilateral about point \(B'\) so that \(BA\) maps to \(B'A'\).

Answer:

First, translate quadrilateral \(ABCD\) so that \(B\) coincides with \(B'\). Then, rotate the translated quadrilateral about \(B'\) until \(BA\) aligns with \(B'A'\). This sequence of a translation followed by a rotation is a sequence of rigid motions that takes \(A\) to \(A'\), \(B\) to \(B'\), \(C\) to \(C'\), and \(D\) to \(D'\).