kite
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.
The pairs of equal sides imply several properties:

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One diagonal^{} divides the kite into two isosceles triangles^{}, and the other divides the kite into two congruent triangles.

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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.

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The diagonals are perpendicular^{}.

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If ${d}_{1}$ and ${d}_{2}$ are the lengths of the diagonals, then the area is
$$A=\frac{{d}_{1}{d}_{2}}{2}$$ Alternatively, if $a$ and $b$ are the lengths of the sides, and $\theta $ the angle between unequal sides, then the area is
$$A=ab\mathrm{sin}\theta .$$ 
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A kite possesses an inscribed circle. That is, there exists a circle that is tangent (touches) the four sides.

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Kites always possess at least one symmetry^{} axis, being the diagonal that divides it into two congruent triangle.
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.
Title  kite 

Canonical name  Kite 
Date of creation  20130322 15:49:22 
Last modified on  20130322 15:49:22 
Owner  yark (2760) 
Last modified by  yark (2760) 
Numerical id  9 
Author  yark (2760) 
Entry type  Definition 
Classification  msc 5100 
Synonym  deltoid 
Related topic  Parallelogram 
Related topic  Quadrilateral 
Related topic  Rhombus 