Public Lessons: Properties of Quadrilaterals
 Properties of Quadrilaterals, Cathy Humphreys

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This lesson is about properties of quadrilaterals and learning to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems.

#### The Core Ideas (standards) addressed by this task are:

• Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.
• Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.
• Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counter examples and indirect proof.
• Identify, formulate and confirm conjectures.
• Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.

#### The idea for the lesson came from two sources:

• The "Shape of Things" Problem of the Month and its related Teacher Notes
• The John Van de Walle mathematics seriesâ€™ investigation of the diagonals of a quadrilateral