Parallelograms (including rectangles and squares)
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The diagonals of a rhombus bisect one another.
The figure is a rectangle.
45 degrees * * * * * The diagonals of a rectange bisect one another but can do so at any angle, x, such that 0<x<180 degrees.
In most shapes the diagonals do not bisect one another. It might be possible to answer the question if it were more specific. To start with, shapes with how many sides?
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.