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Proof in Parallelogram using vectors

Hello everyone,

I need to proof that in a parallelogram, the lines connecting one corner to the middle of its opposite sides split the diagonal of the parallelogram into three equal parts.

I've uploaded an image to clarify see attachment.

(ABCD is the parallelogram, BD is the diagonal, and AE and AF are the lines splitting the diagonal. The rest are lines I thought might be useful, but haven't found out how.

I need to do this proof using vectors. Since it's a parallelogram I know that AB=DC,BC=AD, BD||EF||IJ.

So I need to proof that DH=HG=GB.

So far all my tries lead nowhere and I'm stuck. Any help would be appreciated.

Thanks in advance.

meismo