Question

If $ABCD$ is a parallelogram and $E,F$ are the centroids of $△ABD$ and $BCD$ respectively, then $EF$ equals

• A. $AE$
• B. $BE$
• C. $CE$
• D. $DE$

Answer 1

The correct option is A $AE$

Given, $E$ and $F$ are the centroids of $△ABD$ and $△BCD$
So, $\frac{AE}{EO}=\frac{CF}{FO}=\frac{2}{1}$, i.e.,
$AE=CF=2x$, if $EO=FO=x$
$\Rightarrow$ $EF=EO+FO=x+x=2x$
$\therefore$ $AE=EF=CF$