Task# Congruent Rectangles

Illustrative MathematicsVaries

This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent. Since the two rectangles are congruent, there must be some sequence of translations, rotations, and reflections which will take Rectangle 1 to Rectangle 2 (and vice versa). In practice, there are many possible ways to show a congruence and this should be emphasized in part (a). Students might be encouraged to work on their own to find a congruence before working on the three parts of this problem.