Classifying Quadrilaterals

Prepared by:

Joseph Malkevitch
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001


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The chart below is designed to be part of an activity to help students learn about convex quadrilaterals. The idea is based a paper of the geometer Branko Grünbaum. The job of the student is when a quadrilateral for a particular cell in the matrix exists to draw such a quadrilateral (and perhaps explore different "kinds" of quadrilaterals that might be drawn) and if the quadrilateral does not exist, to use a convincing argument to prove this. For example, the cell in row 4 column 1 can be filled in with a rectangle which is not a square. This is a rich activity in that it requires background knowledge with commonly exhibited quadrilaterals and reasoning skills as well. The mathematical ideas involved extend in a variety of directions.