In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.

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Solution

Given: In a parallelogram ABCD, AM = CN.
To prove: AC and MN bisect each other.
Construction: Join AN and MC.
Proof:
Since, ABCD is a parallelogram.
⇒AB∥DC⇒AM∥NC
Also, AM = CN
(Given)
Thus, AMCN is a parallelogram.
Since, diagonals of a parallelogram bisect each other.
Hence, AC and MN bisect each other.

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