Quandaries
and Queries 

Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? From Carla (teacher) Elementary level (Gr 5) 

Hi Carla, In mathematics we try to be very careful in how we define and use technical language. However not every author uses the same definition and some definitions have changed over time. Euclid, who lived about 2000 years ago would have said that a square is not a rectangle. His definition said explicitly that a square is not a rectangle. The current definition of a rectangle is a parallelogram, all of whose angles are right angles, or something equivalent, and hence a square is a rectangle. This, of course, brings us to your second question, does a parallelogram HAVE to have 4 sides? The answer is yes, a parallelogram is a quadrilateral with both pairs of opposite sides parallel and a quadrilateral has 4 sides. Cheers,Penny 

