Q: What quadrilaterals have diagonals that bisect one another?

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The diagonals of a rhombus bisect one another.

There are two of them and they bisect one another.

The diagonals bisect one another in a rhombus.

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.

They bisect one another.

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.

Yes. The diagonals of any parallelogram bisect each other. A rectangle is a special case of a parallelogram.

No - only one of the diagonals bisects the angles of the shape.

They must meet at right angles and only one of them must bisect the other. (if both bisect one another, the quadrilateral will be a square).

Four straight sides, four right angels, diagonals that bisect one another.