如图,角BAD=角CAD,DE平行AC交AB于E,EF⊥AD交BC于F.求证：角B=角FAC

证明：∵DE‖AC∴∠EDA=∠CAD∵∠CAD=∠EAD∴∠EAD=∠EDA∴EA=ED∵EF⊥AD∴EF是AD的垂直平分线∴FA=FD∴∠FAD=∠FDA∵∠FAD=∠FAC+∠GAD,∠FDA=∠B+∠BAD,∠BAD=∠CAD∴∠FAC=∠B