Kite

Pronunciation: /kaɪt/ Explain

Click on the blue points and drag them to change the figure. Manipulative 1 - Kite Created with GeoGebra.

A kite is a quadrilateral with two sets of adjacent, congruent sides. Properties of a Kite All kites are quadrilaterals. The area of a kite is 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

Step	Diagram	Description
1		Start with a convex kite.
2		Construct the angular bisector of one of the angles connecting congruent sides.
3		Construct the angular bisector of one of the angles connecting non-congruent sides.
4		Label the intersection of bisectors from steps 2 and 3 as O.
5		Construct a line through O perpendicular to one of the sides.
6		Label the intersection of the line constructed in step 5 with the side to which it is perpendicular as P.
7		Construct a circle with center O and radius OP.
Table 1

Geometric Figure Made with Kites

Image	Description
	This tessellation using kites is called a deltoidal trihexagonal tiling. To construct this tessellation, 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 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 deltoidal hexecontrahedron is a polyhedron whose faces are kites.

References

1. McAdams, David E.. All Math Words Dictionary, kite. 2nd Classroom edition 20150108-4799968. pg 105. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

• McAdams, David E.. Kite. lifeisastoryproblem.com. Life is a Story Problem LLC. 8/7/2018. http://www.lifeisastoryproblem.com/explore/kite.html.

Cite this article as:

McAdams, David E. Kite. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/k/kite.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
• Deltoidal Hexecontrahedron: Maxim Razin, https://commons.wikimedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://commons.wikimedia.org/wiki/File:Deltoidalhexecontahedron.jpg.
• Deltoidal Icositetrahedron: Cyp, https://commons.wikimedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://commons.wikimedia.org/wiki/File:Deltoidalicositetrahedron.gif.
• Deltoidal Trihexagon Tiling: R. A. Nonenmacher, https://commons.wikimedia.org. Image licensed under GNU Free Documentation License. https://commons.wikimedia.org/wiki/File:Tiling_Dual_Semiregular_V3-4-6-4_Deltoidal_Trihexagonal.svg.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/29/2018: Corrected spelling. (McAdams, David E.)
8/7/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/4/2010: Added "References", Geometric figure made from kites. (McAdams, David E.)
12/13/2008: Added vocabulary links, properties of a kite, and construction of the incircle of a kite. (McAdams, David E.)
9/16/2008: Initial version. (McAdams, David E.)