# isoseles

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