The opposite sides of a square are parallel and of equal length. Therefore the opposite triangles that the diagonals make are congruent and, as a result, they bisect on another. This is also the reason that they do so in all parallelograms.
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squares
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.
No, for the simple reason that triangles do not have diagonals.
The diagonals of a square bisect each other at 90 degrees
A square. All squares are parallelograms, but not all parallelograms are squares.