Additionally, if a convex kite is not a rhombus, there is another circle, outside the kite, tangent to the lines that pass through its four sides therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral. Therefore, every convex kite is a tangential quadrilateral. Additional propertiesĮvery convex kite has an inscribed circle that is, there exists a circle that is tangent to all four sides. The two interior angles of a kite that are on opposite sides of the symmetry axis are equal. One of the two diagonals of a convex kite divides it into two isosceles triangles the other (the axis of symmetry) divides the kite into two congruent triangles. As is true more generally for any orthodiagonal quadrilateral, the area K of a kite may be calculated as half the product of the lengths of the diagonals p and q:Īlternatively, if a and b are the lengths of two unequal sides, and θ is the angle between unequal sides, then the area is Moreover, one of the two diagonals (the symmetry axis) is the perpendicular bisector of the other, and is also the angle bisector of the two angles it meets. AreaĮvery kite is orthodiagonal, meaning that its two diagonals are at right angles to each other. Kites and isosceles trapezoids are dual: the polar figure of a kite is an isosceles trapezoid, and vice versa. If crossings are allowed, the list of quadrilaterals with axes of symmetry must be expanded to also include the antiparallelograms. Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite (if the axis of symmetry is a diagonal) or an isosceles trapezoid (if the axis of symmetry passes through the midpoints of two sides) these include as special cases the rhombus and the rectangle respectively, which have two axes of symmetry each, and the square which is both a kite and an isosceles trapezoid and has four axes of symmetry. The kites are the quadrilaterals that have an axis of symmetry along one of their diagonals.
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