1.证明：∵正方形ABCD
∴AB=AD,∠ABE=∠ADF=90°
∵AE=AF
∴△ABE≌△ADF
∴BE=DF
2.∵CE=BC-BE=CD-DF=CF,AE=AF,AC=AC
∴△AEC≌△AFC
∴∠EAO=∠FAO
∴AO⊥EF,EO=FO
∵OM=OA
∴四边形AEFM是菱形