Kite
Pronunciation: /kaɪt/ ?
 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
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 noncongruent 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 
Image  Description 
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 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. 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.com. Life is a Story Problem LLC. 20100304. http://www.lifeisastoryproblem.com/explore/kite.html.
Cite this article as:
Kite. 20100304. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/k/kite.html.
Translations
Image Credits
Revision History
20100304: Added "References", Geometric figure made from kites. (
McAdams, David.)
20081213: Added vocabulary links, properties of a kite, and construction of the incircle of a kite (
McAdams, David.)
20080916: Initial version (
McAdams, David.)