# What is a dragon

### Symmetrical dragon

**Definition:** Under a *symmetrical* or *straight kite* (also *Deltoid*, *Trapezoid* or *Pseudorhombus*) one understands a flat convex quadrilateral that is symmetrical to (at least) one diagonal.

From this it follows that the other diagonal is perpendicular to the axis of symmetry and is halved by this. Conversely, these two properties of the diagonals also characterize the symmetrical kites. In contrast to this, one speaks of *leaning* or *oblique kite*when only one diagonal bisects the other, but both are no longer (necessarily) perpendicular to each other.

Obviously, not every symmetrical dragon has a perimeter. But since the angles at A and C are the same because of the symmetry, the two bisectors intersect at a point M on the axis of symmetry and this is the center of the inscribed circle. So every symmetrical kite is a tangent square. By moving A and C in the above picture parallel to the symmetry axis e up to the drawn circle, you get a symmetrical kite that is even a quadrangle of a tendon tangent. Since this is exactly the case when A and C lie on the Thales circle over e, a is created in this case *biorthogonal* symmetrical kite.

There is also *orthogonal* symmetrical kites that only have a right angle. Of course, these then have no radius.

Symmetrical orthogonal kite

from an equilateral and one

isosceles right triangle

Sometimes one also looks at non-convex flat quadrilaterals, where the diagonals are perpendicular to each other and the extension of one diagonal bisects the other. Because of the shape of these quadrilaterals, one speaks of (symmetrical) *Angular kites* or *Arrows*. These can also be generalized to crooked arrows.

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