##
* *Reflection: High Quality Task
Discovering and Proving Polygon Properties Unit Assessment - Section 1: Unit Assessment

I like this proof because there are so many different ways to prove *ABCD* is a parallelogram. This problem gives students the opportunity to use key parallelogram properties to write proofs, an essential idea in this unit.

At this point in the year, my students have proved a lot of different ideas in a lot of different ways. In this particular proof, students used a range of ideas to write the proof: finding pairs of congruent triangles and using CPCTC to ultimately show ABCD had two pairs of congruent sides, two pairs of congruent angles, two pairs of parallel sides, etc.

In discussing this proof after I had returned the tests to students, students easily decided that one particular proof path—proving *ABCD *had diagonals that bisect each other—was the most “elegant” approach. This was a truly special moment in that my students seemed to value the beauty of this simple, yet sound, proof. The students’ discussion rose above the nitty gritty details about parallelogram properties to one that valued and appreciated a novel way of thinking.

*An "Elegant" Proof*

*High Quality Task: An "Elegant" Proof*

# Discovering and Proving Polygon Properties Unit Assessment

Lesson 9 of 9

## Objective: Students will be able to solve problems and write proofs by applying their understanding of polygon properties.

## Big Idea: In this assessment, students take on a variety of questions--true/false, fill in the blank, problem solving, proof--to demonstrate their understanding of polygon properties.

*60 minutes*

##### Similar Lessons

###### Dilation and Similarity Unit Test

*Favorites(2)*

*Resources(20)*

Environment: Rural

###### SAS-sy Triangles

*Favorites(5)*

*Resources(35)*

Environment: Suburban

###### Introduction to Similar Right Triangles

*Favorites(8)*

*Resources(19)*

Environment: Urban

- 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