Proofs: Properties of Parallelograms

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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).