kite

A kite or deltoid is a quadrilateral with two pairs of equal sides, each pair consisting of adjacent sides. Contrast with parallelograms, where the equal sides are opposite.

The pairs of equal sides imply several properties:

• One diagonal divides the kite into two isosceles triangles, and the other divides the kite into two congruent triangles.

• The angles between the sides of unequal length are equal. In the picture, they are both equal to the sum of the blue angle with the red angle.

• The diagonals are perpendicular.

• If $d_1$ and $d_2$ are the lengths of the diagonals, then the area is

  $$A=\frac{d_1{d}_2}{2}$$

  Alternatively, if $a$ and $b$ are the lengths of the sides, and $\theta$ the angle between unequal sides, then the area is

  $$A=ab\sin \theta .$$

• A kite possesses an inscribed circle. That is, there exists a circle that is tangent (touches) the four sides.

• Kites always possess at least one symmetry axis, being the diagonal that divides it into two congruent triangle.

When all the side lengths are the same, the kite becomes a rhombus, and when both diagonals have the same length, the kite becomes a square.