Choose whether the statement is true or false: the diagonals of a parallelogram bisect each other.

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True

False

answer is A.

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Detailed Solution

We have to prove diagonals of parallelogram ABCD bisects each other.
i.e, OA=OC & OB=OD
Now In ΔAOD and ΔBOC
AD=BC [opposite sides are equal]
∠ADO=∠CBO [alternate interior angle]
Similarly ∠DAO=∠BCO
Then, ΔAOD≅ΔBOC by (ASA rule)
So, OA=OC & OB=OB [ By CPCT]
Hence, the given statement is true.

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