Difference between a Square and a Rectangle

Updated on February 22, 2016

So you think you know your squares and rectangles? If so, then you probably already know what quadrilaterals, parallelograms and quadrangles are, but if not, then you might want to know more about these two polygons.

Definitions

Square
A diagram, establishing the properties of a square

Square – In geometry, a square is a four-sided polygon called a quadrilateral. Aside from being called a quadrilateral, it is also labeled as a parallelogram (opposite sides are parallel to each other). But there are many four-sided polygons such as trapezoids, cyclic quadrilaterals, trapeziums etc., so what makes a square different from the others? It is actually a regular quadrilateral, and according to Euclidean geometry (a mathematical system attributed to the Alexandrian Greek mathematician Euclid), it means a square is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides are equal in length).

Properties of a Square

  • All four angles are equal at 90°
  • All four sides are equal in length
  • Opposite sides are parallel
  • The diagonals bisect (divided into two equal parts) its angles
  • The diagonals bisect each other and meet at 90°
  • The diagonals are equal in length

Note: A square can also be defined as a special rectangle, since the opposite sides of a square are parallel to each other, and is also a special case of a rhombus (having four equal sides).

rectangle
A diagram establishing the properties of a rectangle

Rectangle – In Euclidean geometry, a rectangle is also a quadrilateral and as with the square, has four equal angles at 90°. It can also be labeled as a parallelogram since its opposite sides are parallel to each other.

Properties of a Rectangle

  • All four angles are equal at 90°
  • Opposite sides are equal in length
  • Opposite sides are parallel
  • The diagonals are equal in length

Square vs Rectangle

What’s the difference between a square and a rectangle? While it may be a little bit confusing since a square is also a rectangle, there is one difference that makes it easy to distinguish one from the other.

Both a square and a rectangle may have their four angles at 90°, have parallel opposite sides with the same length, and have their diagonals equal in length, but only a square has four sides of equal length. Take note however, a square is also considered a special case of a rectangle, which means a square isn’t primarily a rectangle, but more an example of a rectangle.

To summarize, a square is somewhat a rectangle since it does have all the properties of being a rectangle, but it needs to have its sides equal in measurement to be called a square.

Comparison Chart

SquareRectangle
It is a quadrilateralIt is a quadrilateral
It is a parallelogramIt is a parallelogram
All angles are equal at 90°All angles are equal at 90°
Diagonals are equal in lengthDiagonals are equal in length
Opposite sides are parallelOpposite sides are parallel
All sides are equalOpposite sides are equal

Video

Here is a video that talks about the properties of both square and rectangle.

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