Given: ABCD is a parallelogram

E and F are the centroids of triangle ABD and BCD

Since, the diagonals of parallelogram bisect each other

AO is the median of triangle ABD

And,

CO is the median of triangle CBD

EO= AO (Since, centroid divides the median in the ratio 2:1)

Similarly,

FO = CO

EO + FO = AO + CO

= (AO + CO)

EF = AC

AE = AO

= * AC

= AC

Therefore,

EF = AE