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In this case, the quadrilateral is sometimes a parallelogram.

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Q: If one diagonal of a quadrilateral bisects the other when is the quadrilateral a parallelogram?

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Any quadrilateral that is not a parallelogram can have only one diagonal that is bisected by the other.

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

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Quadrilateral and parallelogram

Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

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No. It could be a kite.

Any quadrilateral that is not a parallelogram can have only one diagonal that is bisected by the other.

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

isn't it a rhombus ? the ones that are like a slanted square ? because there are no right angles but each diagonal bisects the corners.

Yes: one of them, but the other diagonal does not.

No, a parallelogram is not another kind of quadrilateral.

No, they do not. Only the longer diagonal bisects the shorter diagonal.

Not necessarily.

Yes, in the figure of a kite one diagonal bisects the other. They do not bisect each other.

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parallelogram and polygon * * * * * Wrong. A quadrilateral need not be a parallelogram. A kite is a quadrilateral but nobody with the slightest mathematical knowledge would call a kite a parallelogram!

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