Geometric kite

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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.

Contents

1 Properties
2 Other kites
3 Notes
4 See also

Properties

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=\frac]

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

[A=\,]

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

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.

Geometric kite

Properties

Other kites

Notes

See also