![]() The cyclic quadrilaterals may equivalently defined as the quadrilaterals in which two opposite angles are supplementary (they add to 180°) if one pair is supplementary the other is as well. The right kites are exactly the kites that are cyclic quadrilaterals, meaning that there is a circle that passes through all their vertices. The right kites have two opposite right angles. The self-crossing quadrilaterals include another class of symmetric quadrilaterals, the antiparallelograms. These include as special cases the rhombus and the rectangle respectively, and the square, which is a special case of both. Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite, with a diagonal axis of symmetry or an isosceles trapezoid, with an axis of symmetry through the midpoints of two sides. Like kites, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent. By avoiding the need to consider special cases, this classification can simplify some facts about kites. The remainder of this article follows a hierarchical classification rhombi, squares, and right kites are all considered kites. When classified partitionally, rhombi and squares would not be kites, because they belong to a different class of quadrilaterals similarly, the right kites discussed below would not be kites. All equilateral kites are rhombi, and all equiangular kites are squares. Classified hierarchically, kites include the rhombi (quadrilaterals with four equal sides) and squares. Quadrilaterals can be classified hierarchically, meaning that some classes of quadrilaterals include other classes, or partitionally, meaning that each quadrilateral is in only one class. ![]() According to Olaus Henrici, the name "kite" was given to these shapes by James Joseph Sylvester. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a hovering bird and the sound it makes.
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