?$ (1)$?證明：∵?$BD\perp m，$??$CE\perp m，$?∴?$∠BDA=∠AEC = 90°$?
∵?$∠BAC = 90°，$?∴?$∠BAD+∠CAE = 90°$?
又∵?$∠BAD+∠ABD = 90°，$?∴?$∠CAE=∠ABD$?
?$ $?在?$\triangle ABD$?和?$\triangle CAE$?中
?$ \begin {cases}∠BDA=∠AEC\\∠ABD=∠CAE\\AB = CA\end {cases}$?
∴?$\triangle ABD≌\(chéng)triangle CAE(\mathrm {AAS})$?
∴?$BD = AE，$??$AD = CE$?
∵?$DE = AD+AE，$?∴?$DE = BD + CE$?
?$ (2)$?解：?$DE = BD + CE，$?理由：
∵?$∠BDA=∠BAC=α$?
∴?$∠DBA+∠BAD=∠BAD+∠CAE = 180°-α$?
∴?$∠DBA=∠EAC$?
?$ $?在?$\triangle ABD$?和?$\triangle CAE$?中
?$ \begin {cases}∠BDA=∠AEC\\∠DBA=∠EAC\\AB = CA\end {cases}$?
∴?$\triangle ABD≌\(chéng)triangle CAE(\mathrm {AAS})$?
∴?$BD = AE，$??$AD = CE$?
∵?$DE = AE+AD，$?∴?$DE = BD + CE$?
