The diagonals of a parallelogram bisect each other.

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Solution

from the figure-
In $△ A B D$ and $△ C B D$
$A D = B C$
$C D = A B$
$∠ D A B = ∠ B C D$ [Opposite angle]

Therefore, $△ A B D ≅$ $△ C B D$
Hence, the diagonals of a parallelogram bisect each other.

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Q. Diagonals of a parallelogram bisect each other.

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Prove logically the diagonals of a parallelogram bisect each other. Show conversely that a quadrilateral in which diagonals bisect each other is a parallelogram.

Which of the given statements is incorrect

1.Diagonals of the parallelogram bisect each other.
2.If the Diagonals of a quadrilateral bisect each other,it is a parallelogram.
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Q. Prove that the diagonals of a parallelogram bisect each other.

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The diagonals of a parallelogram bisect each other.

from the figure-In △ABD and △CBDAD=BCCD=AB∠DAB=∠BCD [Opposite angle]Therefore, △ABD≅△CBDHence, the diagonals of a parallelogram bisect each other.

from the figure-
In $△ A B D$ and $△ C B D$
$A D = B C$
$C D = A B$
$∠ D A B = ∠ B C D$ [Opposite angle]

Therefore, $△ A B D ≅$ $△ C B D$
Hence, the diagonals of a parallelogram bisect each other.