A kite or deltoid is a quadrilateralMathworldPlanetmath with two pairs of equal sides, each pair consisting of adjacent sidesMathworldPlanetmathPlanetmath. Contrast with parallelogramsMathworldPlanetmath, where the equal sides are opposite.

The pairs of equal sides imply several properties:

  • One diagonalMathworldPlanetmath divides the kite into two isosceles trianglesMathworldPlanetmath, 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 perpendicularMathworldPlanetmathPlanetmathPlanetmath.

  • If d1 and d2 are the lengths of the diagonals, then the area is


    Alternatively, if a and b are the lengths of the sides, and θ the angle between unequal sides, then the area is

  • A kite possesses an inscribed circle. That is, there exists a circle that is tangent (touches) the four sides.

  • Kites always possess at least one symmetryMathworldPlanetmath axis, being the diagonal that divides it into two congruent triangle.

When all the side lengths are the same, the kite becomes a rhombusMathworldPlanetmath, and when both diagonals have the same length, the kite becomes a square.

Title kite
Canonical name Kite
Date of creation 2013-03-22 15:49:22
Last modified on 2013-03-22 15:49:22
Owner yark (2760)
Last modified by yark (2760)
Numerical id 9
Author yark (2760)
Entry type Definition
Classification msc 51-00
Synonym deltoid
Related topic Parallelogram
Related topic Quadrilateral
Related topic Rhombus