vi tam giac ABC = tam giac HIK
\Rightarrow goc B = goc I (1)
vi tam giac HIK = tam giac ACB
\Rightarrowgoc I = goc C (2)
tu (1)(2)\Rightarrowgoc B = goc C
vay trong tam giac ABC co goc B = goc C>->->->-
xet tam giac ANB=tam giac AMC co:
AM la canh chung (1)
AB=AB(gt) (2)
BM=MC(vi M la trung diem cua BC) (3)
tu (1)(2)(3)\Rightarrow tam giac AMB= tam giac AMC
\Rightarrowgoc AMB=goc AMC (2 goc tuong ung)
ma goc AMC+ goc AMB=[TEX]180^o[/TEX]
\Rightarrowgoc AMC= goc AMB =[TEX]180^o[/TEX]/2 = [TEX]90^o[/TEX]
\RightarrowAM vuong goc voi BC