Any quadrilateral that is not a parallelogram can have only one diagonal that is bisected by the other.
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In this case, the quadrilateral is sometimes a parallelogram.
A quadrilateral is an object formed by four straight lines - two of which meet at an angle. A diagonal is one of the lines which go from one angle to the one other angle in the quadrilateral which it is not already connected to. If the angles of the quadrilateral are A, B, C and D, and A is connected by a straight line to B and D then the diagonal is a line between A and C. A--B | \ | D--C
You need to know the lengths of the sides and at least one angle or the length of a diagonal.
If both pairs of opposite sides are parallel: A Rectangle, or a Square. If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid. If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral
a hexagon