cho tam giac ABC vuong tai A ( AB < AC ) tren canh BC lat diem K / AB = BK . Goi H la TD AK . Keo dai BH cat AC ai I
a neu goc ABC = 60 . tinh so do ACB
b cm 2 tam giac ABH = KBH . tu do suy ra HK vuong vs BI
c qua K ke duong thang song song AC , cat BH va AB lan luot N va D . cm KA la tia pg IKD
d ke AM vuong goc vs BC tai M . cm 3 diem A , N .M thang hang
a) Xét \(\Delta ABC\)có \(\widehat{A}=90^o\)
\(\Rightarrow\widehat{ABC}+\widehat{ACB}=90^o\)
\(\Rightarrow60^o+\widehat{ACB}=90^o\)
\(\Rightarrow\widehat{ACB}=90^o-60^o=30^o\)
b) Xét \(\Delta ABH\)và \(\Delta KBH\)có:
AB = BK (gt)
BH là cạnh chung
AH = KH (H là trung điểm của AK)
\(\Rightarrow\Delta ABH=\Delta KBH\left(c.c.c\right)\)
\(\Rightarrow\widehat{AHB}=\widehat{KHB}\)(2 góc tương ứng)
Mà \(\widehat{AHB}+\widehat{KHB}=180^o\)(kề bù)
\(\Rightarrow\widehat{AHB}=\widehat{KHB}=\frac{180^o}{2}=90^o\)
\(\Rightarrow AK\perp BH\)hay \(HK\perp BI\)
c)
