Kite

Pronunciation: /kaɪt/ ?

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Manipulative 1: Kite Created with GeoGebra

A kite is a quadrilateral with two sets of adjacent, congruent sides. Click on the blue points in manipulative 1 and drag them to change the figure.

Properties of a Kite

  • All kites are quadrilaterals.
  • The area of a kite is A=(1/2)pq where p is the length of one diagonal and q is the length of the other diagonal. See manipulative 1.
  • The diagonals of a kite are perpendicular.
  • Opposite vertices of a kite are congruent.
  • An incircle can be inscribed into any convex kite.
  • One of the diagonals of a convex kite divides the kite into two isosceles triangles. The other diagonal of a convex kite divides the kite into two congruent triangles.

Construction of the Incircle of a Kite

StepDiagramDescription
1Kite with vertices labeled A, B, C, and D with A opposite B and C opposite D.Start with a convex kite.
2Kite from step 1 with the angle bisector of ACB.Construct the angular bisector of one of the angles connecting congruent sides.
3Kite from step 2 with the angle bisector of CBD.Construct the angular bisector of one of the angles connecting non-congruent sides.
4Kite from step 3 with intersection of the angle bisectors labeled 'O'.Label the intersection of bisectors from steps 2 and 3 as O.
5Kite from step 4 with a line through 'O' perpendicular to BD.Construct a line through O perpendicular to one of the sides.
6Kite from step 5 with the intersection of the perpendicular line and BC labeled 'P'.Label the intersection of the line constructed in step 5 with the side to which it is perpendicular as P.
7Kite from step 6 with a circle with center O and radius OP.Construct a circle with center O and radius OP.
Table 1

Geometric Figure Made with Kites

ImageDescription
Deltoidal trihexagon tiling: Divide hexagons into six kites by drawing segments from the midpoint of each side to the center of the hexagon. Tile the hexagons so that three hexagons share each vertex.
Image courtesy R. A. Nonenmacher. Image licensed under GNU Free Documentation License. Click on the image for more information.
This tesselation using kites is called a deltoidal trihexagonal tiling. To construct this tesselation, divide each hexagon into six kites by drawing a segment from the midpoint of each side to the center. Then tesselate the divided hexagon so that three hexagons share each vertex.
A spinning deltoidal icositetrahedron.gif. A deltoidal icositetrahedron is a polyhedron whose faces are kites. Click to print a net of a deltoidal icositetrahedron to cut out and paste together.
A spinning deltoidal hexecontahedron. A deltoidal hexecontrahedron is a polyhedron whose faces are kites. Click to print a net of a deltoidal hexecontrahedron to cut out and past together. This geometric net is courtesy Wolfram Mathworld.

More Information

  • McAdams, David. Kite. lifeisastoryproblem.org. Life is a Story Problem LLC. 2010-03-04. http://www.lifeisastoryproblem.org/explore/kite.html.

Cite this article as:


Kite. 2010-03-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/k/kite.html.

Translations

Image Credits

Revision History


2010-03-04: Added "References", Geometric figure made from kites. (McAdams, David.)
2008-12-13: Added vocabulary links, properties of a kite, and construction of the incircle of a kite (McAdams, David.)
2008-09-16: Initial version (McAdams, David.)

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