**Classifying Quadrilaterals**

Prepared by:

Joseph Malkevitch

Mathematics and Computing Department

York College (CUNY)

Jamaica, New York 11451-0001

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk/__

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.