Given,

ABCD is a parallelogram

E & F are centroids of ∆ABD & ∆BCD respectively

We know that diagonals of parallelogram bisect each other & centroid of a median divides it in 2:1

So, in ∆ABD ,

=

Similarly,

= AO = CO

=

From equations (i) & (ii)

EO = FO

EF = 2 FO…………..(III)

AE = CF……(IV)

From equation (i)

= AE =

=AE =

= AE =

= AE =

=

=

=

= AE= EF