SWBAT prove that rectangles are parallelograms with congruent diagonals and also identify key characteristics of special parallelograms like squares, rhombi and rectangles.

Students will complete and present a parallelogram proof to their peers and provide feedback on these presentations.

5 minutes

This Do Now serves as a quick formative assessment of students' knowledge of special cases of parallelograms, more specifically, a square. This lesson is packed with great activities so this Do Now has been shortened to 5 minutes.

20 minutes

In this lesson, there is extra time for you to finish the coordinate geometry proofs from the prior lesson, Calling All Quads. Included in the student notes for Calling All Quads, on page 2, there are two proofs. These two proofs are given in the students notes with scaffolds and can be completed by students in pairs or in small groups. Some of these proofs are quite challenging, and require students to think critically through each step (MP1 and MP7).

New teachers may want to consider how to modify this lesson. For example, Practice Proof #2 could have some or all of the steps removed, alternatively this can be scaffolded more by working as a whole class to complete the distance and slope formula calculations, as needed.

20 minutes

30 minutes

Students will be assigned to a group and asked to prove one of the 5 challenging, parallelogram-related proofs in the Student Presentations Handout/Homework. Each group will work together to complete each challenge proof (MP1), and will then either type or hand write their proof for review by the entire class (MP3).

This activity works best when students have 20-30 minutes to work on their proof in class, and then try all of the other proofs for homework. Then in the next lesson, Review of Pretty Polygons, students will have had a chance to construct their arguments for their proof and can also critic the proofs of their peers.

You can also ask students to shoot a video of their proof and make this into a mini-project.