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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 Parallelogram s, where the equal sides are opposite.


PROPERTIES


The pairs of equal sides imply many properties:

  • The Angle s 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.



  • If d_1 and d_2 are the lengths of the diagonals, then the area is

    • :A= rac{d_1d_2}{2}

Alternatively, if a and b are the lengths of the sides, and heta the angle between unequal sides, then the area is
:A={a b \sin heta}\,

  • 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