Editing Rectangle (section)

==Properties==

===Symmetry===
A rectangle is [[Cyclic polygon|cyclic]]: all [[Corner angle|corner]]s lie on a single [[circle]].

It is [[equiangular polygon|equiangular]]: all its corner [[angle]]s are equal (each of 90 [[Degree (angle)|degrees]]).

It is isogonal or [[vertex-transitive]]: all corners lie within the same [[symmetry orbit]].

It has two [[line (geometry)|line]]s of [[reflectional symmetry]] and [[rotational symmetry]] of order 2 (through 180°).

===Rectangle-rhombus duality===
The [[dual polygon]] of a rectangle is a [[rhombus]], as shown in the table below.<ref>de Villiers, Michael, "Generalizing Van Aubel Using Duality", ''Mathematics Magazine'' 73 (4), Oct. 2000, pp. 303–307.</ref>

{|class="wikitable" style="text-align:center"
|-
!Rectangle !! Rhombus
|-
|All ''angles'' are equal.
||All ''sides'' are equal.
|-
|Alternate ''sides'' are equal.
||Alternate ''angles'' are equal.
|-
|Its centre is equidistant from its ''[[Vertex (geometry)|vertices]]'', hence it has a ''[[circumcircle]]''.
||Its centre is equidistant from its ''sides'', hence it has an ''incircle''.
|-
|Two axes of symmetry bisect opposite ''sides''.
||Two axes of symmetry bisect opposite ''angles''.
|-
|Diagonals are equal in ''length''.
||Diagonals intersect at equal ''angles''.
|}
* The figure formed by joining, in order, the midpoints of the sides of a rectangle is a [[rhombus]] and vice versa.

===Miscellaneous===
A rectangle is a [[rectilinear polygon]]: its sides meet at right angles.

A rectangle in the plane can be defined by five independent [[Degrees of freedom (mechanics)|degrees of freedom]] consisting, for example, of three for position (comprising two of [[Translation (geometry)|translation]] and one of [[rotation]]), one for shape ([[Aspect ratio#Rectangles|aspect ratio]]), and one for overall size (area).

Two rectangles, neither of which will fit inside the other, are said to be [[Comparability|incomparable]].