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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