Special Cases
If all four sides of a kite have the same length (that is, if the kite is equilateral), it must be a rhombus.
If a kite is equiangular, meaning that all four of its angles are equal, then it must also be equilateral and thus a square.
The kites that are also cyclic quadrilaterals (i.e. the kites that can be inscribed in a circle) are exactly the ones formed from two congruent right triangles. That is, for these kites the two equal angles on opposite sides of the symmetry axis are each 90 degrees. These shapes are called right kites and they are in fact bicentric quadrilaterals (below to the left).
There are only eight polygons that can tile the plane in such a way that reflecting any tile across any one of its edges produces another tile; one of them is a right kite, with 60°, 90°, and 120° angles. The tiling that it produces by its reflections is the deltoidal trihexagonal tiling.
A right kite |
An equidiagonal kite inscribed in a Reuleaux triangle |
Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles π/3, 5π/12, 5π/6, 5π/12 (above to the right).
Read more about this topic: Kite (geometry)
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