Q. 174.5( 2 Votes )

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

B. BE

C. CE

D. DE

Answer :

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

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