2. Let $\displaystyle N$ be the midpoint of $\displaystyle \overline{BE}.$
$\displaystyle \overline{MN}\parallel\overline{BH}\implies\overli ne{NM}\perp\overline{AH}\implies\overline{AM}\perp \overline{HN}.$ Finally $\displaystyle \overline{HN}\parallel\overline{CE}\implies\overli ne{AM}\perp\overline{EC}~\blacksquare$