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Problem of the Month

The Department of Mathematics poses an occasional mathematics problem which will appear on bulletin boards near the Department offices in Drew Science. It will also appear here. Generally, solutions will not require any advanced mathematics. We welcome solutions from students, faculty, staff and strangers who happen to walk or surf by.

The best student solutions will be posted and awared a cash prize of $5, or whatever loose change we have in our pockets, and the winner will have her/his name published in a prestigious location.

Solutions must be, above all, correct but preference will be given to elegant and well-written solutions. Partial solutions are also welcome.

Solutions should be submitted to Professor Guetter in DS 123A or sent to MB 140.

Department of Mathematics Problem
December, 2011

Choose a point P on one side of an arbitrary triangle. Draw a line parallel to a second side, crossing the third side at Q. Construct any arallelogram using PQ as one edge and a segment on the third side as another edge. (The parallelogram with solid edges in the diagram below.) Construct a second parallelogram in the same manner, interchanging the roles of the two sides not containing P. (The parallelogram with the dashed edges in the diagram below.) Show that the two parallelograms have the same area.
triangle

Previous Problems of the Month
October, 2011
November, 2011