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Geometry/Making Four Non-Parallelogram Congruent Quadrilaterals


Can you draw two straight lines across a square to form four quadrilaterals that aren't a parallelogram of any kind? Note: squares and rectangles are parallelograms. The shapes need to be congruent.

Hi Taimur,

Draw a square with a cross in the middle, so as to subdivide the square into four congruent small squares.  Now pivot the cross so that instead of landing on the midpoint of each of the square's sides, it lands a quarter of the way.  The result is as desired.

For easier visualization, draw a square on a Cartesian plane with vertices on (0,0), (4,0), (4,0), and (4,4).  Make a line between (3,0) and (1,4).  Make a second line between (0,1) and (4,3).

This is a neat little question.  Feel free to ask a follow-up if you want some insight on how to arrive at the above answer.

Thanks for asking,


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Azeem Hussain


I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.


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