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Prove using vectors: The diagonals of a ...

Prove using vectors: The diagonals of a quadrilateral bisect each other iff it is a parallelogram.

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Let `ABCD` is a parallelogram and the position vectors of `A,B,C,D` be `veca,vecb,vecc,vecd` respectively.
`vec{AB}=vec{DC}`
`implies vecb-veca=vecc-vecd`
`implies vecb+vecd=veca+vecc`
`implies 1/2(vecb+vecd)=1/2(veca+vecc)`
`implies` Diagonals of a parallelogram bisects each other.
Conversely,
Let diagonals of a quadrilateral `ABCD` with position vectors of `A,B,C,D` be `veca,vecb,vecc,vecd` respectively, bisects each other.
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