Editing Kite (geometry) (section)

== Definition and classification ==
[[File:Deltoid.svg|thumb|Convex and concave kites]]
A kite is a [[quadrilateral]] with [[reflection symmetry]] across one of its diagonals. Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides.{{r|halsted|devilliers-adventures}} A kite can be constructed from the centers and crossing points of any two intersecting [[circle]]s.{{r|idiot}} Kites as described here may be either [[Convex polygon|convex]] or [[Concave polygon|concave]], although some sources restrict ''kite'' to mean only convex kites. A quadrilateral is a kite [[if and only if]] any one of the following conditions is true:
* The four sides can be split into two pairs of adjacent equal-length sides.{{r|devilliers-adventures}}
* One diagonal crosses the midpoint of the other diagonal at a right angle, forming its [[perpendicular bisector]].{{r|usiskin-griffin}} (In the concave case, the line through one of the diagonals bisects the other.)
* One diagonal is a line of symmetry. It divides the quadrilateral into two congruent triangles that are mirror images of each other.{{r|devilliers-adventures}}
* One diagonal [[Angle bisector|bisects]] both of the angles at its two ends.{{r|devilliers-adventures}}
Kite quadrilaterals are named for the wind-blown, flying [[kite]]s, which often have this shape{{r|beamer|alexander-koeberlein}} and which are in turn named for [[kite (bird)|a hovering bird]] and the sound it makes.{{r|nuncius|liberman}} According to [[Olaus Henrici]], the name "kite" was given to these shapes by [[James Joseph Sylvester]].{{r|henrici}}

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. Classified hierarchically, kites include the [[rhombus|rhombi]] (quadrilaterals with four equal sides), [[square (geometry)|squares]],{{r|devilliers-role}} and [[Apollonius quadrilateral]]s (in which the products of opposite sides are equal).{{r|harras}} All [[equilateral polygon|equilateral]] kites are rhombi, and all [[equiangular polygon|equiangular]] kites are squares. When classified partitionally, rhombi and squares would not be kites, because they belong to a different class of quadrilaterals; similarly, the [[right kite]]s discussed below would not be kites. The remainder of this article follows a hierarchical classification; rhombi, squares, and right kites are all considered kites. By avoiding the need to consider special cases, this classification can simplify some facts about kites.{{r|devilliers-role}}

Like kites, a [[parallelogram]] also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent. Any [[simple polygon|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. These include as special cases the [[rhombus]] and the [[rectangle]] respectively, and the square, which is a special case of both.{{r|halsted}} The self-crossing quadrilaterals include another class of symmetric quadrilaterals, the [[antiparallelogram]]s.{{r|alsina-nelson}}