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# Geometry/Making Four Non-Parallelogram Congruent Quadrilaterals

Question
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.

Azeem

Geometry

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#### Azeem Hussain

##### Expertise

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

##### Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.