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# square

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 $r\sqrt{2}$.

Related:

Quadrilateral, Parallelogram, Rectangle, Rhombus, ParallelogramLaw, RegularPolygon

Type of Math Object:

Definition

Major Section:

Reference

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51-00*no label found*

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## Comments

## redundancy

Phrase "is the regular 4-gon, that is," is not a part of definition.

It is a part of properties.

And url of "regular" is inapropriate.

This phrase should be just removed from definition as quadrilateral is enough.

It should be good also to cite Euclid, Book I, Definitions item 22:

a right-angled equilateral quadrilateral figure