Cho\(\Delta ABC\)co AB=AC va M la trung diem cua BC.Tren tia doi cua tia BC lay D.Tren tia doi cua CB lay E sao cho BD=CE
a)Chung minh:\(\Delta ABD=\Delta ACE\).Tu do suy ra AM la tia phan giac cua \(\widehat{DAE}\)
b)Ke \(BK\perp AD\left(K\in AD\right)\).Tren tia doi cua BK lay diem H sao cho BH=AE.Tren tia doi cua AM lay diem N sao cho AN=CE.Chung minh\(\widehat{MAD}=\widehat{MBH}\)
c)Chung minh;\(DN\perp DH\)
a) Có: AB=AC
\(\Rightarrow\Delta ABC\) là tam giác cân tại A
\(\Rightarrow\widehat{ABC}=\widehat{ACB}\)
Mà \(\widehat{ABD}+\widehat{ABC}=180^o\) (kề bù)
\(\widehat{ACE}+\widehat{ACB}=180^o\)(kề bù)
\(\Rightarrow\widehat{ABD}=\widehat{ACE}\)
Xét \(\Delta ABD\) và \(\Delta ACE\) có:
\(AB=AC\left(gt\right)\)
\(\widehat{ABD}=\widehat{ACE}\left(cmt\right)\)
\(BD=CE\left(gt\right)\)
\(\Rightarrow\Delta ABD=\Delta ACE\left(c.g.c\right)\)
