Provide the Requested Proof $\mathrm { ABC }$ Be an Isosceles Triangle With

Essay

Provide the requested proof.
-Let $\mathrm { ABC }$ be an isosceles triangle with $\angle \mathrm { B } \cong \angle C$ . Suppose that $M$ is a point on $B C$ such that $\overline { \mathrm { AM } }$ is perpendicular to $\overline { \mathrm { BC } }$ . Prove that $\mathrm { M }$ is the midpoint of $\overline { \mathrm { BC } }$ .