Creating Quadrilaterals from Quadrilaterals

  • Creating Quadrilaterals from Quadrilaterals

    Wayne Nirode
    Students create rules to form new quadrilaterals from existing ones, use dynamic geometry software to construct and make conjectures about these, and attempt to prove their conjectures.
    Apart of high school geometry is devoted to the study of parallelograms in the context of proving some of their properties using congruent triangles (CCSSI 2010). The typical high school geometry book’s chapter on quadrilaterals focuses on parallelograms (e.g., their properties, proving that a given quadrilateral is a parallelogram, and special parallelograms) with an additional section about trapezoids and kites. I wanted to go beyond what is required by the Common Core State Standards for Mathematics and what is in the usual textbook chapter on quadrilaterals and give my students the opportunity to pose and investigate their own questions about quadrilaterals. I devised a project in which my students created rules to form a new quadrilateral starting from a special quadrilateral: parallelogram, rhombus, rectangle, square, kite, trapezoid, isosceles trapezoid, and cyclic quadrilateral. They used Dynamic Geometry Software (DGS) to construct, explore, and conjecture; and, last, they proved their conjectures either synthetically or analytically.
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