In this lesson, students find rigid transformations that show two figures are congruent and consider why two figures are not congruent. As students compare features of two shapes on a coordinate plane, they observe that having corresponding side lengths that are equal is not enough to determine that two figures are congruent. Students use differences in features, such as angle measures, side lengths, perimeters, or the order of congruent sides, to construct arguments that two figures are not congruent (MP3). 

This lesson also asks students to consider more complex shapes with curved sides. Unlike polygons, curved shapes may not be defined by a set of vertices, so more care is needed to determine congruence. Students identify corresponding points on curved figures and compare the distances between those points. The focus here is on the fact that the distance between any pair of corresponding points of congruent figures must be the same. Because there are too many pairs of points to consider, this fact is mainly a criterion for showing that two figures are not congruent. Only one example of different distances between pairs of corresponding points is enough to conclude that two figures are not congruent.

In today’s activities, students are introduced to the idea of math norms as expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Students then consider what norms would connect and support the math actions the class recorded so far in the Math Community Chart.