They are 4 sided quadrilaterals such as a square, a rectangle, a rhombus, a parallelogram and a kite.
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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?
The diagonals of a square bisect each other at 90 degrees
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
Square, rhombus and a kite have diagonals that bisect each other at 90 degrees