# 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

• 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

StepDiagramDescription
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

ImageDescription 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.
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

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

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

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/29/2018: Corrected spelling. (McAdams, David E.)