已知,如图,△ABC中,AB=AC,CD⊥AB于D 求证 ∠BAC=2∠DCB

证明：在△ABC中,因为AB=AC,那么2 ∠ABC+∠BAC=180°在,△BCD中,CD⊥AB,那么∠ABC+∠DCB =90°2∠ABC+2∠DCB =180°=2 ∠ABC+∠BAC化简得∠BAC=2∠DCB