Prove by vector method that the quadrilateral whose diagonal bisect each other is a parallelogram.

My Attempt

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I have tried till here. Then please help to complete the proof.


Given conditions are
$\vec{CM} = \vec{MA}$
$\vec{MB} = \vec{OM}$

It can be seen using the triangle law of addition that
$\vec{CB} = \vec{CM} + \vec{MB}$
$\vec{OA} = \vec{OM} + \vec{MA}$

It can clearly be seen that $\vec{CB} = \vec{OA}$ (substitute the first 2 equations into any one of the last 2 equations). And by the theorem "If two sides of a quadrilateral are parallel and equal, the quadrilateral is a parallelogram (see the $4^{th}$ characterisation here)", the result is proved.


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