Which parallelograms are dragon squares?

Rhombuses are (symmetrical) dragon squares

• A kite square is what most people associate with the figure of the well-known kite: Each two adjacent sides are the same length, one diagonal is the axis of symmetry and divides the other diagonal.
• In addition, the two diagonals of these figures, which are called symmetrical or straight dragon squares in mathematics, are perpendicular to each other.

Against this background, can there actually be parallelograms that simultaneously (!) Dragon squares are, because in a parallelogram two opposite sides are each the same length and parallel?

• Both conditions can be met well if all sides of the parallelogram are of the same length, i.e. a diamond (and in the extreme case a square) is present.
• You will not associate a rhombus or a square with a dragon square when you look at it, but both figures have all of the mentioned conditions.
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Draw a diamond - the math expert shows how it's done

The diamond is a special parallelogram, i.e. a geometric ...

Conclusion: diamonds (and special squares) are parallelograms and symmetrical kite quadrilaterals at the same time.

All parallelograms are crooked kite squares

Besides the well-known symmetrical dragon square, she knows mathematics further dragon squares, namely crooked resp. sloping.

• You can get a good idea of ​​these figures by looking at a kite in the sky from an oblique perspective.
• Such crooked dragon squares have only one mathematical condition: one diagonal bisects the other, but the two are no longer perpendicular to each other.
• However, it is precisely this halving condition that every parallelogram fulfills, so that, based on this mathematical definition, all parallelograms are also dragon quadrilaterals, albeit crooked.

Conclusion: If you take the definition of a general kite square as a basis, then any parallelogram is also a kite square - even if it doesn't look like that, of course.