# Proofs: Properties of Parallelograms

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## Objective

Students will be able to solve problems and write proofs using special parallelogram properties.

#### Big Idea

In a group challenge activity, students hold each other accountable as they apply special parallelogram properties to solve problems and write proofs.

## Polygon Progression: Tasks 2 and 3

60 minutes

In today's group challenge I ask my students to apply their understanding of the properties of parallelograms and special parallelograms to solve leveled problems (MP1).  I plan to hold each group accountable for ensuring that every individual understands and can represent the entire group’s thinking. I do this by letting students know that when the whole group is ready to check in with me, I will shuffle all the papers behind my back and choose one at random, and that person must explain on behalf of their group.

When I launch the challenge, I make sure to highlight the Group Work Behaviors poster to remind groups of the actions they can take to work effectively.  I will also post a list of reminders and strategies on the whiteboard for students to refer to as they work:

• Don’t make assumptions that can’t be justified
• Reason logically to write your proof:
• Start with only what’s given to prove the properties they think/know to be true
• Recall that there are multiple ways to show congruence
• Congruent triangles: SSS, SAS, ASA, AAS
• CPCTC
• Angle relationships

When groups have finished working on all five levels of the group challenge, I move them onto the last task of Polygon Progression, which requires them to write proofs about parallelogram properties.

## Polygon Practice Proofs

30 minutes

At this point in the unit, students are preparing for the unit assessment. I feel it is important to provide additional opportunities to practice writing proofs.  In Polygon Practice Proofs, I give students two proofs that require them to apply or prove parallelogram properties (MP2, MP7).