∴∠ AEB =∠ CFE = 90 (vertical definition)

∫∠CFE is the outer angle of △CFB (known).

∴∠ Fcb +∠ FBC =∠ CFE = 90 (the outer angle of a triangle is equal to the sum of two non-adjacent inner angles).

∠∠ABC =∠Abe+∠FBC = 90 (known)

∴∠FCB=∠ABE (complementary angles of the same angle are equal)

∵ In △ Abe and △FBC:

{∠ AEB = ∠ CFE (certification)

∠FCB =∠ Abe (certification)

AB=AC (known)

∴△ABE≌△FBC(AAS)

∴AE=FB, CF=BE (the corresponding sides of congruent triangles are equal).

∴EF=BE-FB=CF-AE (equivalent substitution)