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# Calling All Quads Again

Lesson 6 of 8

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

#### Resources

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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.

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#### Student Presentations

*30 min*

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.

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- UNIT 1: Introduction to Geometry: Points, Lines, Planes, and Angles
- UNIT 2: Line-sanity!
- UNIT 3: Transformers and Transformations
- UNIT 4: Tremendous Triangles
- UNIT 5: Three Triangle Topics
- UNIT 6: Pretty Polygons
- UNIT 7: MidTerm Materials
- UNIT 8: Circles
- UNIT 9: 3-D Shapes and Volume
- UNIT 10: Sweet Similar Shapes
- UNIT 11: Trig Trickery
- UNIT 12: Finally Finals