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Q: Is it true if the diagonals of a quadrilateral bisects each other then the quaderateral is a parrallelogram?

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Not necessarily.

There is no quadrilateral on that list with diagonals that bisect each other.

yes it bisects.

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

No, but the diagonals of a square does bisects its interior angles.

No. It could be a kite.

The longer diagonal bisects the shorter diagonal.

In this case, the quadrilateral is sometimes a parallelogram.

The diagonals bisect one another in a rhombus.

not necessarily. because the diagonals of a trapezium also bisect each other and it is not a parallelogram. in order for the quadrilateral to become a parallelogram, the opposite angles of it must be equal, and the opposite sides must be equal too. the angles formed by the two diagonals( four in number) also must be equal if they are opposite angles not alternating angles.that's it pal

Bisect: Yes At 90 degrees: No

This cannot be proven, because it is not generally true. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. And conversely, the diagonals of any parallelogram bisect each other. However not every parallelogram is a rhombus.However, if the diagonals are perpendicular bisectors, then we have a rhombus.Consider quadrilateral ABCD, with diagonals intersecting at X, whereAC and BD are perpendicular;AX=XC;BX=XD.Then angles AXB, BXC, CXD, DXA are all right angles and are congruent.By the ASA theorem, triangles AXB, BXC, CXD and DXA are all congruent.This means that AB=BC=CD=DA.Since the sides of the quadrilateral ABCD are congruent, it is a rhombus.

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