Question

已知在三角形ABC中,AB等于AC,O是三角形ABC内一点,且BO等于OC.求证,AO垂直BC

Answer 1

连接AO,AB=AC,∠ACB=∠ABC；OB=OC,∠OCB=∠OBC∠ACO=∠ACB-∠OCB,∠ABO=∠ABC∠OBC.∠ACO=∠ABO.AB=AC,OB=OC△ACO≌△ABO.∠BAO=∠CAOAO是等腰三角形的顶角平分线,所以也是高AO⊥BC