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In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".
As a trigonal bipyramidal molecule undergoes Berry pseudorotation, it proceeds via an intermediary stage with the square pyramidal geometry.Thus even though the geometry is rarely seen as the ground state, it is accessed by a low energy distortion from a trigonal bipyramid.
Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles – a right kite.A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also ex-tangential.
The theorem can be applied to a complex (self-intersecting) quadrilateral. In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral.
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A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry.The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals.
As an example, we consider a glass square of a certain thickness with a letter "F" written on it to make the different positions distinguishable. In order to describe its symmetry, we form the set of all those rigid movements of the square that do not make a visible difference (except the "F").
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles.It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle.