∴∠ 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)