Geometry
# Congruent and Similar Triangles

$\triangle ABC$ above, $\angle A={66}^\circ,$ $M$ is the midpoint of side $\overline{BC},$ and $D$ and $E$ are the feet of perpendicular drawn from $M$ to $\overline{AB}$ and $\overline{AC},$ respectively. If $\lvert{\overline{MD}}\rvert=\lvert{\overline{ME}}\rvert,$ what is the measure of $\angle CME ?$

In**Note:** The above diagram is not drawn to scale.

$ABC$ and $DEF$, if we know that $AB = EF, BC = DE$ and $\angle ABC = \angle DEF$, are the triangles congruent?

In triangles