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If you are clever you will know that a trapezium does not bisect.
It was the French mathematician Rene Descartes who introduced coordinated geometry by means of the Cartesian plane which consist of an horizontal x axis and vertical y axis that are perpendicular to each other and bisect each other at the origin whose coodinates are (0, 0)
Usually, a parallelogram with not bisect other shapes.
It depends on what you mean by bisect. All rectangles have diagonals that bisect the other one. Only certain rectangles (Squares) have diagonals that bisect its vertex, the ninety degree angle.
Opposite angles do not bisect any shapes.