(1)∵∠BME+∠BEM=∠BME+∠FMC=135°,∴∠BEM=∠FMC,∴ΔBEM∽ΔCMF.
∴
又∠B=∠EMF=45°∴ΔEBM∽ΔEMF;
(2)若EF∥BC,则EM=FM,∴BE=MB=√2,∴AE=2-√2,∴EF=√2(2-√2)=2√2-2
(1)∵∠BME+∠BEM=∠BME+∠FMC=135°,∴∠BEM=∠FMC,∴ΔBEM∽ΔCMF.
∴
又∠B=∠EMF=45°∴ΔEBM∽ΔEMF;
(2)若EF∥BC,则EM=FM,∴BE=MB=√2,∴AE=2-√2,∴EF=√2(2-√2)=2√2-2