1955 AMC 12 Question 48 - thichhoctoan.com

Question 48

Given triangle $ABC$ with medians $\overline{AE},$ $\overline{BF},$ $\overline{CD};$ $\overline{FH}$ parallel and equal in length to $\overline{AE};$ $\overline{BH}$ and $\overline{HE}$ are drawn; $\overline{FE}$ extended meets $\overline{BH}$ in $G.$ Which one of the following statements is not necessarily correct?

$AEHF$ is a parallelogram
$\overline{HE}=\overline{HG}$
$\overline{BH}=\overline{DC}$
$\overline{FG}=\dfrac34\overline{AB}$
$\overline{FG}$ is a median of triangle $BFH$