## Polygon Progression - Section 1: Polygon Progression: Tasks 2 and 3

# Proofs: Properties of Parallelograms

Lesson 7 of 9

## 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.

*90 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.

#### Resources

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#### Polygon Practice Proofs

*30 min*

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**).

#### Resources

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Review Angle Relationships to Begin Conjecturing About Polygons
- LESSON 2: Interior and Exterior Angle Sum of Polygons
- LESSON 3: Going Deeper with Interior and Exterior Angles
- LESSON 4: Focus on Justification: Interior and Exterior Angles
- LESSON 5: Kite & Trapezoid Properties and Midsegments of Triangles & Trapezoids
- LESSON 6: Properties of Parallelograms and Special Parallelograms
- LESSON 7: Proofs: Properties of Parallelograms
- LESSON 8: Review: Polygon Properties
- LESSON 9: Discovering and Proving Polygon Properties Unit Assessment