Chứng minh tam giác AMC = tam giác BMN

$$\begin{gathered} \mathrm{Cho} ∆\mathrm{ABC} \mathrm{vuông} \mathrm{tại} \mathrm{A}. \mathrm{Gọi} \mathrm{M} \mathrm{là} \mathrm{trung} \mathrm{điểm} \mathrm{AB}, \mathrm{trên} \mathrm{tia} \mathrm{đối} \mathrm{của} \mathrm{tia} \mathrm{MC} \mathrm{lấy} \mathrm{điểm} \mathrm{N} \mathrm{sao} \mathrm{cho} \mathrm{MN}=\mathrm{MC}. \mathrm{Chứng} \mathrm{minh}: \\ \mathrm{a}) ∆\mathrm{AMC}=∆\mathrm{BMN} \\ \mathrm{b}) \mathrm{BN}\perp \mathrm{AB} \mathrm{và} \mathrm{BN} //\mathrm{AC} \\ \mathrm{c}) \widehat{\mathrm{CAN}} = \widehat{\mathrm{NBC}} \end{gathered}$$