Prove that the sides opposite to equal angles of a triangle are equal.

In an isosceles triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ with $\mathrm{A}\mathrm{B}=\mathrm{A}\mathrm{C},\mathrm{}\mathrm{D}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{}\mathrm{E}$ are points on $\mathrm{B}\mathrm{C}$ such that $\mathrm{B}\mathrm{E}=\mathrm{C}\mathrm{D}$ (see figure). Show that $\mathrm{A}\mathrm{D}=\mathrm{A}\mathrm{E}.$

In the figure, $\mathrm{A}\mathrm{D}=\mathrm{A}\mathrm{E}$ and $\mathrm{D}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{}\mathrm{E}$ are points on $\mathrm{B}\mathrm{C}$ such that $\mathrm{B}\mathrm{D}=\mathrm{E}\mathrm{C}$. Prove that $\mathrm{A}\mathrm{B}=\mathrm{A}\mathrm{C}$.