In this lesson, students explore what it means for shapes to be “the same.” First, students consider figures that are mirror images of each other and decide what properties these figures share. Next, students compare pairs of figures that may or may not be the same size and shape and construct arguments about which pairs of figures are the same (MP3). Students are then introduced to the term congruent. They learn that two figures are congruent if there is a sequence of translations, rotations, and reflections that moves one to the other. Finally, students consider the specific properties of area and perimeter for various rectangles and use tools, such as rulers, protractors, and tracing paper, to identify congruent shapes (MP5). 

As students work to determine whether pairs of shapes are “the same,” or congruent, they may notice properties that occur in congruent pairs of figures but not in different pairs. These  properties include:

• Corresponding sides of congruent figures are the same length.
• Corresponding angles of congruent figures are the same measure.
• Congruent figures have the same perimeter and the same area.

These observations support the definition of “congruent” figures, since one congruent figure can be taken to the other by a rigid transformation. An important consequence of this definition is that while having a different perimeter or area is enough to determine that two figures are not congruent, having the same perimeter or area is not sufficient to show that two figures are congruent. 

Today’s math community building time has two goals. The first is for students to make a personal connection to the math actions chart and to share on their Cool-down the math action that is most important to them. The second is to introduce the idea that the math actions that students have identified will be used to create norms for their mathematical community in upcoming lessons.