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: