Kite (geometry)

A kite quadrilateral ( in mathematics: Deltoid ) is a planar quadrilateral in which

  • A diagonal symmetry axis,

Or ( equivalently )

Often just called a dragon square and the non- convex shape as an arrow square the convex shape of the deltoids. ( The term " dragon square" refers to the form of many kites. )

A special dragon square is the rhombus (also hash): it is an equilateral deltoid.

A generalization of the kite is the oblique (inclined ) dragon, in which only requires that one diagonal is bisected by the other. The deltoid is then a straight dragon.

Properties

For each deltoid applies:

  • The diagonals are perpendicular to each other ( they are orthogonal: the deltoid is an ortho diagonal square)
  • The diagonal AC bisects the diagonal BD
  • The opposed angle in the corners B and D are the same size
  • The diagonal through the corner points A and C halved in these angles

For each convex deltoid applies:

  • It has an inscribed circle and is therefore a tangent quadrilateral.
  • It also has a radius when the two corner angles are equal ( in B and D ) right angle (90 °).

With the notation of the figure applies:

The diagonal AC is the symmetry axis and bisects the diagonal BD. It divides the quadrilateral ABCD into two congruent mirror-symmetrical triangles (ABC and ACD). The diagonal BD divides the square into two isosceles triangles (ABD and BCD). The interior angles at B and D are equal. The angles at A and C are bisected by the diagonal.

Formulary

The area of ​​a quadrilateral kite can be easily determined from the lengths of the diagonals e and f:

The volume is calculated as:

Convex set Orthogonality Perimeter
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