Kite (Geometry)

In geometry a kite, or deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the sides of equal length are opposite. The geometric object is named for the wind-blown, flying kite (itself named for a bird), which in its simple form often has this shape. Equivalently, a kite is a quadrilateral with an axis of symmetry along one of its diagonals. Any quadrilateral that has an axis of symmetry must be a kite or an isosceles trapezoid (including the special cases rhombus and rectangle respectively, and the square which is both). Kites and isosceles trapezoids are dual: the polar figure of a kite is an isosceles trapezoid, and vice versa. A kite, as defined above, may be either convex or concave, but the word "kite" is often restricted to the convex variety. A concave kite is sometimes called a "dart" or "arrowhead", and is a type of pseudotriangle. The Properties of KITE Every kite is orthodiagonal: the two diagonals are perpendicular. Half the product of the lengths of the diagonals is the area of a kite:  Alternatively, if a and b are the lengths of two unequal sides, and θ is the angle between unequal sides, then the area is ab sin θ. One diagonal divides a (convex) kite into two isosceles triangles; the other (the axis of symmetry) divides the kite into two congruent triangles. Two interior angles at opposite vertices of a kite are equal. Every convex kite has an inscribed circle; that is, there exists a circle that is tangent to all four sides. Therefore, every convex kite is a tangential quadrilateral. Additionally, if a convex kite is not a rhombus, there is another circle, outside the kite, tangent to all four sides, suitably extended. For every concave kite there exist two circles tangent to all four (possibly extended) sides: one is interior to the kite and touches the two sides opposite from the concave angle, while the other circle is exterior to the kite and touches the kite on the two edges incident to the concave angle. The kites are exactly the quadrilaterals that are both orthodiagonal and tangential. In a tangential quadrilateral, the two line segments connecting opposite points of tangency have equal length if and only if the quadrilateral is a kite. The perimeter of a kite:

To find the perimeter of a kite, just add up all the lengths of the sides:

The area of a kite:

To find the ae as multiplying by 1/2):

The sides and angles of a kite: There are two sets of adjacent sides (next to each other) that are the same length (congruent.) There is one set of congruent angles.  These are opposite of each other and are between sides that are different lengths. On this one, it's kind of hard to put this stuff into words that aren't confusing...   So, look at the picture!

The diagonals of a kite:  The intersection of the diagonals of a kite form   90 degree (right) angles.  This means that they are perpendicular.The longer diagonal of a kite bisects the shorter one.  This means that the longer diagonal cuts the shorter one in half. External Link: http://www.coolmath.com/reference/kites.html http://en.wikipedia.org/wiki/Kite_(geometry)

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Written by Mahendra Almazzzzzz

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