△ ABC is an isosceles right triangle, and m is the midpoint of the hypotenuse BC.
∴am⊥bc,am=bm,△abm≌△cam,∠mac=∠mba=45
∠∠b = 45,DF⊥BF.
∴△BFD is an isosceles right triangle.
∵DF⊥AB,DE⊥AC,∠BAC=90?
A quadrilateral is a rectangle.
∴ BF = FD = AE and ∠ FBD = 45.
∫△BFM is equal to△△△ AEM (SAS).
∴∠BMF=∠AME,FM=EM
∴∠FME=∠FMA+∠AME=∠BMF+∠FMA=90
△ FME is an isosceles right triangle.