A Rectangle
A Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. Another name is
equiangular quadrilateral, since equiangular means that all of its angles are equal (360/4 = 90). It can
also be defined as a parallelogram containing a right angle. The term oblong is occasionally used to
refer to a non-square rectangle.
A rectangle with vertices ABCD would be denoted as ABCD.The word rectangle comes from the Latin
rectangulus, which is a combination of rectus (right) and angulus (angle).A so-called crossed rectangle
is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along
with the two diagonals.
It is a special case of an antiparallelogram, and its angles are not right angles. Other geometries, such as
spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and
equal angles that are not right angles.
Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a
rectangle by polygons.
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Characterizations:- A convex quadrilateral is a rectangle if and only if it is any one of the following:
[4][5]
a parallelogram with at least one right angle
an equiangular parallelogram
a parallelogram with diagonals of equal length
a parallelogram ABCD where triangles ABD and DCA are congruent
a quadrilateral which has four right angles
an equiangular quadrilateral
Classification:- Traditional hierarchy
A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.
A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both
pairs of opposite sides are parallel and equal in length.
A trapezium is a convex quadrilateral which has at least one pair of parallel opposite sides.
A convex quadrilateral is
Alternative hierarchy
De Villiers defines a rectangle more generally as any quadrilateral with axes of symmetry through each
pair of opposite sides.[6] This definition includes both right-angled rectangles and crossed rectangles.
Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another
which is the perpendicular bisector of those sides, but, in the case of the crossed rectangle, the first axis
is not an axis of symmetry for either side that it bisects.
Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger
class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These
quadrilaterals comprise isosceles trapezia and crossed isosceles trapezia (crossed quadrilaterals with the
same vertex arrangement as isosceles trapezia).
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