Kite (geometry)

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This article is about the geometric shape. For the flying object, see Kite.

In geometry, a kite, or deltoid, is a quadrilateral with two pairs of equal adjacent sides. Technically, the pairs of sides are disjoint congruent and adjacent. This is in contrast to a parallelogram, where the equal sides are opposite. The geometric object is named for the wind-blown, flying kite (which is itself named for a bird), which in its simple form often has this shape.

1 Properties
2 Special cases
3 See also
4 External links

[edit] Properties

The pairs of equal sides imply many properties:

The angles between the sides of unequal length are equal. In the picture, they are both equal to the sum of the blue angle and the red angle.
The diagonals are perpendicular.
One diagonal divides the kite into two isosceles triangles, and the other divides the kite into two congruent triangles
Kites always posses at least one symmetry axis; that axis is the diagonal that divides it into two congruent triangles
A kite possesses an inscribed circle; that is, there exists a circle that is tangent to all four sides.
If <math>d_1</math> and <math>d_2</math> are the lengths of the diagonals, then the area is

Alternatively, if <math>a</math> and <math>b</math> are the lengths of the sides, and <math>\theta</math> the angle between unequal sides, then the area is

<math>A={a b \sin\theta}\,</math>

[edit] Special cases

When all the sides are the same length, the kite becomes a rhombus.
When, additionally, both diagonals have the same length, the kite becomes a square.
A non-convex deltoid is called a dart, rather than a kite.