In geometry, a kite or deltoid is a quadrilateral, with two pairs of equal sides, each pair consisting of adjacent sides. Contrast with parallelograms, where the equal sides are opposite. A simpler definition is A kite is a quadrilateral with two pairs of disjoint congruent adjacent sides.

Properties

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The pairs of equal sides imply many properties:

• One diagonal divides the kite into two isosceles triangles, and the other divides the kite into two congruent triangles
• The angles between the sides of unequal length are equal. In the picture, they are both equal to the sum of the blue angle with the red angle.
• The diagonals are perpendicular.
• If $d\_1$ and $d\_2$ are the lengths of the diagonals, then the area is

$A=\backslash frac\{d\_1d\_2\}\{2\}$

Alternatively, if $a$ and $b$ are the lengths of the sides, and $\backslash theta$ the angle between unequal sides, then the area is

$A=\{a\; b\; \backslash sin\backslash theta\}\backslash ,$

• A kite possesses an inscribed circle. That is, there exists a circle that is tangent to (touches) the four sides.
• Kites always posses at least one symmetry axis, being the diagonal that divides it into two congruent triangles

When all the side lengths are the same, the kite becomes a rhombus, and when both diagonals have the same length, the kite becomes a square.

Other kites

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A kite is also an object that opposes the force of the wind with the tension of a string held by the operator; see kite flying. The geometric term was inspired by the name of this object (itself based on kite (bird)), which in its simple form is often a quadrilateral.

Notes

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See also

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• Kite flying

kites | Quadrilaterals

Drachenviereck | Deltoide | Aquilone (geometria) | דלתון | Deltoid | Vlieger (meetkunde) | Draken (Geometrie) | Deltoid | Дельтоид | 鷂形