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Lesson plan

Lesson 12: Proofs about Quadrilaterals

teaches Common Core State Standards HSG-CO.C.11 http://corestandards.org/Math/Content/HSG/CO/C/11
teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1

Lesson 12: Proofs about Quadrilaterals

In a previous lesson students used strips and fasteners to make conjectures and practice proofs about quadrilaterals. In this lesson students prove the important result that all rectangles are parallelograms. Then groups of students tackle different relationships among quadrilaterals and their diagonals. This requires reasoning from definitions such as:

  • rectangle is a quadrilateral with four right angles.
  • rhombus is a quadrilateral with four congruent sides.

Throughout the lesson students move from making conjectures, to making specific statements to be proved, to writing a proof, to critiquing a proof. When students have to determine the given information and draw their own diagram students are making sense of problems (MP1).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

Lesson overview

  • 12.1 Warm-up: Play with Parallelograms  (10 minutes)
  • 12.2 Activity: From Conjecture to Proof (15 minutes)
  • 12.3 Activity: Checking a Proof (10 minutes)
    • Includes "Are you Ready for More?" extension problem
  • Lesson Synthesis
  • 12.4 Cool-down: A Proof In Time Saves Nine  (5 minutes) 

Learning goals:

  • Comprehend a conjecture and express it (in writing) as a specific statement to prove.
  • Critique others' reasoning (in spoken and written language) about quadrilaterals.
  • Prove (in writing) theorems about quadrilaterals.

Learning goals (student facing):

  • Let’s prove theorems about quadrilaterals and their diagonals.

Learning targets (student facing):

  • I can critique a proof about quadrilaterals.
  • I can prove theorems about quadrilaterals.
  • I can rewrite a conjecture so it is specific enough to prove.

Required materials:

  • 1-inch strips cut from card stock with evenly-spaced holes
  • Geometry toolkits
  • Metal paper fasteners


  • rectangle - A quadrilateral with four right angles.

  • rhombus - A quadrilateral with four congruent sides.

  • Access the complete Geometry Course glossary.


  • This lesson builds on the standards: CCSS.HSG-CO.B.8MS.G-CO.8CCSS.HSG-CO.C.9MS.G-CO.9MO.G.CO.B.7MO.G.CO.C.8
  • This lesson builds towards the standards: CCSS.HSG-CO.C.11MS.G-CO.11MO.G.CO.C.10






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