Reflection: Grappling with Complexity Properties of Parallelograms and Special Parallelograms - Section 4: Practice: Determining Parallelograms


“Is one pair of congruent, parallel sides enough to guarantee a quadrilateral is a parallelogram?”

Okay, I have to admit that this tormented my students far more than any other. They seemed convinced that this idea was true, but their reasoning heavily relied on arguments like, “the opposite sides can’t be parallel AND congruent unless it’s a parallelogram!  It’s the only way for this to work.” I think that my students knew their arguments lacked currency, yet, at the time, they seemed unable to supply more evidence. 

To accomplish my objectives for the lesson, I needed my students to connect their argument to concrete evidence.  I prompted them with questions like:

  • How can we build our argument on our prior knowledge?
  • How did we show sides or angles were congruent in the past?

These questions helped my students to recall relevant information. But, I am still wondering how to prepare my students to prompt themselves to consider this without my assistance?       

  Is this enough? Furthering our understanding of parallelogram properties.
  Grappling with Complexity: Is this enough? Furthering our understanding of parallelogram properties.
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Properties of Parallelograms and Special Parallelograms

Unit 8: Discovering and Proving Polygon Properties
Lesson 6 of 9

Objective: Students will be able to apply angle relationships and properties of isosceles triangles and trapezoids in a proof.

Big Idea: In the Logical Road Map, students will make sense of multiple pathways to writing a proof.

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Math, Geometry, polygons (Determining Measurements), properties of polygons, reasoning and proof, parallelogram
  90 minutes
prop of parallel li
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