Question

cho tam giac ABC co AB bang AC bang 5 cm ; BC bang 6 cm . ke AH vuong BC , h thuoc bc 

  a , chung minh HB bang HC va BAH bang CAH 

  B, tinh do dai AH 

  c, ke HM vuong AB tai M , ke HN vuong AC tai N . Chung minh tam giac MHN la tam giac can 

   d, ke tia Bx vuong BA , ke Cy vuong AC ; hai tia Bx va Cy cat nhau tai I .Chung minh AI vuong goc voi BC

 

Answer 1

tu ve hinh : 

a, AC = AB => tamgiac ABC can tai A (dn)

=> goc ABC  = goc ACB (tc) 

xet tam giac ABH va tamgiac ACH co : goc AHC = goc AHB do AH | BC (gt)

=>  tam giac ABH = tamgiac ACH (ch - gn)            (1)

b, tamgiac AHB vuong tai H do AH | BC (gt)

=> AB² = AH² + BH² 

 (1) =>  BH  = HC ma BC = 6 (gt)=> BH = 3

BA = 5 (gt)

=> AH²  = 5² - 3²

=> AH²  = 16

=> AH = 4 do AH  > 0

c, xet tamgiac BMH va tamgiac NCH co : goc BMH = goc NCH = 90^o do MH | AB va HN | AC (gt)

goc ABC = goc ACB (cmt) va BH = HC (cmt)

=>  tamgiac BMH = tamgiac NCH (ch - gn) 

=> MH = HN (dn)

=> tamgiac MNH can tai H (dn)

d, cm theo truong hop ch - gn di, moi tay qa

Answer 2

                       Giải

( Bạn tự vẽ hình nhé )

a, \(AB=AC\)  \(\Rightarrow\)\(\Delta ABC\)  cân tại A 

\(\Rightarrow\widehat{ABC}=\widehat{ACB}\) 

Xét \(\Delta ABH\) và \(\Delta ACH\) có : \(\widehat{AHC}=\widehat{AHB}\)  do \(AH\perp BC\)

\(\Delta ABH=\Delta ACH\)              (1) [ đpcm]

b, \(\Delta AHB\) vuông tại H do \(AH\perp BC\)

 \(\Rightarrow AB^2=AH^2+BH^2\)

Từ  (1) suy ra  BH  = HC mà BC = 6 nên BH = 3

\(\Rightarrow\)BA = 5 

\(\Rightarrow AH^2=5^2-3^2\)

\(\Rightarrow AH^2=25-9\)

\(\Rightarrow AH^2=16\)

\(\Rightarrow AH=\sqrt{16}\)

\(\Rightarrow AH=4cm\)

\(\Rightarrow\) AH = 4cm do AH  > 0

c, Xét \(\Delta BMH\) và \(\Delta NCH\) có :\(\widehat{BMH}=\widehat{NCH}=90^0\) do \(MH\perp AB\) va \(HN\perp AC\)

 \(\Rightarrow\widehat{ABC}=\widehat{ACB}\)và \(BH=HC\)

\(\Rightarrow\Delta BHM=\Delta NCH\)  

\(\Rightarrow MH=HN\)

\(\Rightarrow\Delta MNH\) cân tại H \(\left(đpcm\right)\)

d, ...