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[parent] kite (Definition)

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.

\includegraphics[scale=0.75]{GeometricKite.eps}

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
    \begin{displaymath}A=\frac{d_1d_2}{2}\end{displaymath}

    Alternatively, if $a$ and $b$ are the lengths of the sides, and $\theta$ the angle between unequal sides, then the area is
    \begin{displaymath}A={a b \sin\theta}.\end{displaymath}

  • 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.




"kite" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: parallelogram, quadrilateral, rhombus

Other names:  deltoid
Keywords:  quadrilateral, parallelogram, rhombus, square, geometry

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Cross-references: square, rhombus, axis, symmetry, tangent, circle, inscribed, area, perpendicular, sum, length, angles, triangles, congruent, isosceles triangles, divides, diagonal, properties, imply, opposite, parallelograms, adjacent sides, sides, quadrilateral

This is version 6 of kite, born on 2006-03-30, modified 2006-10-20.
Object id is 7789, canonical name is Kite.
Accessed 4339 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

Pending Errata and Addenda
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wikientry by drini on 2006-03-30 17:24:39
The initial version is based on Wikipedia's "kite" entry, version
22:55, 30 March 2006
http://en.wikipedia.org/w/index.php?title=Geometric_kite&oldid=46234068

Contributors list: http://en.wikipedia.org/w/index.php?title=Geometric_kite&action=history

I created the image, the original source (can be edited with free tool Inkscape) it's at
http://en.wikipedia.org/wiki/Image:GeometricKite.svg


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G -----> H G
p \ /_ ----- ~ f(G)
 \ / f ker f
 G/ker f 
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