ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF=
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