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.
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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 <math>d_1</math> and <math>d_2</math> are the lengths of the diagonals, then the area is
- <math>A=\frac{d_1d_2}{2}</math>
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>
- A kite posseses an inscribed circle. That is, there exists a circle that is tangent (touches) the four sides.
- Kites always posses 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.
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.
Notes
See also
es:Deltoide he:דלתון it:Aquilone (geometria) nl:Vlieger (meetkunde) pl:Deltoid ru:Дельтоид zh:鷂形