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If you are clever you will know that a trapezium does not bisect.
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.
Bisect a segment is to divide the line segment into 2