In this lesson, students prove two statements about the diagonals of parallelograms.

• The diagonals of a parallelogram bisect each other.
• If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Students learn a new strategy for looking for structure (MP7) by working backward from the statement they are trying to prove to the given statements. Students also encounter a situation where they could use overlapping triangles, which can be challenging. Students learn techniques for redrawing or marking diagrams to help them see additional triangles to use in congruence proofs. As students prove theorems about parallelograms, they are explicitly practicing proof techniques and looking for structure.

One of the activities in this lesson works best when each student has access to internet-enabled devices because students will benefit from seeing the relationship in a dynamic way.