#### Answer

$\mathbb{ASSUME}$ that $\overrightarrow{\rm FH}$ $\bot$ $\overleftrightarrow{\rm EG}$. Then $\angle$3 $\cong$ $\angle$4 and m$\angle$3 $=$ m$\angle$4. But it is given that m$\angle$3 $\gt$ m$\angle$4, which leads to a contradiction. Then the assumption $\overrightarrow{\rm FH}$ $\bot$ $\overleftrightarrow{\rm EG}$ must be false and it follows that $\overrightarrow{\rm FH}$ is not perpendicular to $\overleftrightarrow{\rm EG}$.

#### Work Step by Step

Work cannot be shown for a proof. Logic is the only work done in such instances. Such work takes place mentally, and therefore cannot be shown.