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# Review Angle Relationships to Begin Conjecturing About Polygons

Lesson 1 of 9

## Objective: SWBAT apply their existing knowledge of angle relationships (parallel lines postulate, triangle sum) to form conjectures about the properties of a regular hexagon.

Since this is planned to be the first lesson of the new semester, I make sure to give students feedback on their performance on the midterm exam. I take time to briefly discuss some of the most commonly missed problems. In doing so, I keep in mind that I am trying to foster a growth mindset. What's done, is not really done. It is important to be able to apply what we have learned so far. We will begin this process today.

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#### Quick Angles Review

*25 min*

The ability to applying existing knowledge of both **angle relationships** and **triangle properties** is a pre-requisite for the first lesson of this unit on **polygon properties**. In this small review task, students recall the **triangle sum theorem** and **properties of isosceles triangles**. I want them to be able to apply this knowledge to discover something new about regular hexagons.

When I debrief these problems with my students I emphasize the important properties and vocabulary they will need in the regular hexagon exploration. I pay more attention to this today than I would otherwise, because my students have had two weeks off for winter break. It is time to restart their mathematical search engines.

#### Resources

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At the end of today's lesson, since this is the first day of the new semester, I want my students to leave knowing that as of today they all have a fresh start in the class. For tonight's homework assignment, I ask them to write a letter to me about their goals for the second half of the year. In the assignment, I ask my students include at least two specific things they plan to continue doing and/or changing, knowing that I will hold them accountable to these actions as I help them to acquire a growth mindset.

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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