In \(\triangle ABC\) 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 \(\angle CME ?\)

Note: The above diagram is not drawn to scale.

Triangles \(ABC\) and \(DEF\) are congruent, that is, \( \triangle ABC \cong \triangle DEF .\) If \(AB=3\), \(BC=4\) and \(CA=5 \), what is the length of \(DE\)?

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

In triangles \(ABC \) and \(DEF\), if we know that \( \angle ABC = \angle DFE \), \( \angle BCA = \angle FED \) and \( \angle CAB = \angle EDF \), are the triangles congruent?

Triangles \(ABC\) and \(DEF\) are congruent. If \( AB = DE\), \( BC = EF \), \( \angle ABC = 37 ^ \circ \) and \( \angle EDF = 39 ^ \circ \), what is the measure (in degrees) of \( \angle EFD\)?