A quadrilateral.
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Yes, in the figure of a kite one diagonal bisects the other. They do not bisect each other.
Square, rhombus or a kite.
a 4 sided figure * * * * * A four sided figure need no be a parallelogram. Think of a kite!
Not usually. In Geometry a kite is defined as a quadrilateral figure having two pairs of equal adjacent sides.
It depend on what kind of kite you have. Two points are symmetric with respect to a point iff it is the midpoint of the line segment joining them. So if you have like a dragon kite, then probably not, but if you have a traditional dizmond kite, then yes.