In previous lessons, students have proven shortcuts for triangle congruence. In this lesson, students apply the triangle congruence theorems to parallelograms in order to generate and prove congruence theorems for parallelograms. Students have an opportunity to make sense of problems and persevere in solving them (MP1) as they take the general question “When are parallelograms congruent?” and figure out how to generate cases to test. As students continue to test the cases rigorously and then prove their conjectures, they are expressing regularity in repeated reasoning (MP8).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Generate (in writing) conjectures about quadrilateral congruence.
- Prove (in writing) quadrilateral congruence theorems using rigid transformations.
- Let’s investigate how congruence for quadrilaterals is similar to and different from congruence for triangles.
- I can use rigid transformations to prove quadrilaterals are congruent.
- I can write conjectures about quadrilateral congruence.