?$(2)$?證明：延長?$F D$?至點(diǎn)?$G，$?使?$DG = DF，$?連接?$BG，$??$EG$?
∵點(diǎn)?$D$?是?$BC$?的中點(diǎn)，∴?$DB = DC$?
在?$?BDG $?和?$?CDF {中}$?
?$ \begin {cases}{DB=DC}\\{∠BDG=∠CDF}\\{DG=DF}\end {cases}$?
∴?$?BDG≌?CDF(S AS)$?
∴?$BG = CF$?
∵?$ED⊥F D，$?∴?$∠EDF=∠EDG=90°$?
在?$?EDF $?和?$?EDG {中}$?
?$ \begin {cases}{ED=ED}\\{∠EDF=∠EDG}\\{DF=DG}\end {cases}$?
∴?$?EDF≌?EDG(S AS)$?
∴?$EF = EG$?
∵在?$?BEG {中}，$??$BE + BG＞EG$?
∴?$BE + CF＞EF$?
?$(3)$?解：?$DM⊥BM$?且?$DM = BM，$?理由：
延長?$DM$?到點(diǎn)?$N，$?使?$MN = DM，$?連接?$CN，$??$BN$?
根據(jù)?$AD = DE，$??$AB = BC，$??$∠EDA=∠ABC=90°$?
可證?$∠E=∠BAC=45°，$??$∠DAB=90°$?
由?$(1)$?可證?$?DEM≌?NCM(S AS)，$?則?$DE = NC，$??$∠MCN=∠E=45°$?
可證?$AD = CN，$??$∠BCN=90°，$?可證?$?BCN≌?BAD(S AS)$?
則?$BN = BD，$?可得?$∠DBN=90°$?
根據(jù)?$DM = NM，$?可得?$BM⊥DM，$??$DM = BM$?
