In this lesson, students use rigid transformations and compare features to decide whether shapes with curves are congruent. Unlike polygons, curved shapes may not be defined by a set of vertices, so more care is needed to determine congruence. Students begin the lesson by constructing mathematical questions about an image of ovals. This helps them  make sense of applying congruence to curved shapes (MP1). 

Students then deepen their understanding by identifying corresponding points on curved figures and comparing 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 the optional activity, students have additional practice determining congruence. They study figures made of several different parts and construct arguments about whether those figures are congruent (MP3). It is not enough that the constituent parts be congruent. They must also be in the same configuration and the same distance apart. This follows from the definition of “congruence” because rigid motions do not change distances between points. If figure 1 is congruent to figure 2, then the distance between any pair of points in figure 1 is equal to the distance between the corresponding pair of points in figure 2.

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.