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.
It divides the quadrilateral into two congruent triangles that are mirror images of each other. (In the concave case, the line through one of the diagonals bisects the other.)
One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector.The four sides can be split into two pairs of adjacent equal-length sides.A quadrilateral is a kite if and only if any one of the following conditions is true: Kites as described here may be either convex or concave, although some sources restrict kite to mean only convex kites. A kite can be constructed from the centers and crossing points of any two intersecting circles. Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides. Kites also form the faces of several face-symmetric polyhedra and tessellations, and have been studied in connection with outer billiards, a problem in the advanced mathematics of dynamical systems.Ī kite is a quadrilateral with reflection symmetry across one of its diagonals. Kites of two shapes (one convex and one non-convex) form the prototiles of one of the forms of the Penrose tiling. The quadrilateral with the greatest ratio of perimeter to diameter is a kite, with 60°, 75°, and 150° angles. They include as special cases the right kites, with two opposite right angles the rhombi, with two diagonal axes of symmetry and the squares, which are also special cases of both right kites and rhombi. The convex kites are exactly the quadrilaterals that are both orthodiagonal and tangential.
Įvery kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). A kite may also be called a dart, particularly if it is not convex. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. A kite, showing its pairs of equal-length sides and its inscribed circle.
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