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square (Definition)

A square is the regular 4-gon, that is, a quadrilateral whose 4 angles and 4 sides are respectively equal. Each angle of a square must be a right angle. This implies a square is a parallelogram that is both a rhombus and a rectangle at the same time.

Notice, however, that if a quadrilateral has its 4 sides equal, we cannot generally say it is a square, since it might be a rhombus as well.

If $ r$ is the length of a side, the diagonals of a square (which are equal since it's a rectangle too) have length $ r\sqrt{2}$.

\includegraphics{square}




"square" is owned by drini. [ full author list (2) | owner history (1) ]
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See Also: quadrilateral, parallelogram, rectangle, rhombus, parallelogram law, regular polygon


Attachments:
compass and straightedge construction of square (Algorithm) by Wkbj79
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Cross-references: diagonals, length, rectangle, rhombus, parallelogram, implies, right angle, sides, angles, quadrilateral, regular
There are 45 references to this entry.

This is version 3 of square, born on 2001-12-12, modified 2006-11-03.
Object id is 1086, canonical name is Square.
Accessed 10671 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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