\(\Delta ABC\) vuông tại \(A\)\(AH...">
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a: Xét ΔABH vuông tại H và ΔCBA vuông tại A có

góc B chung

=>ΔABH đồng dạng với ΔCBA

b: ΔABC vuông tại A

mà AH là đường cao

nên HA^2=HB*HC

c: AI/IH=BA/BH

EC/AE=BC/BA

mà BA/BH=BC/BA

nên AI/IH=EC/AE
=>AI*AE=IH*EC

6 tháng 5 2020

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6 tháng 5 2020

ABCHKIEF

a) 

Xét \(\Delta\)ABC và \(\Delta\)HBA có: 

^BAC = ^BHA ( = 90 độ ) 

^ABC = ^HBA ( ^B chung ) 

=> \(\Delta\)ABC ~ \(\Delta\)HBA 

b) AB = 3cm ; AC = 4cm 

Theo định lí pitago ta tính được BC = 5 cm 

Từ (a) => \(\frac{AB}{BH}=\frac{BC}{AB}\Rightarrow BH=\frac{AB^2}{BC}=1,8\)

c) Xét \(\Delta\)AHC và \(\Delta\)AKH có: ^AKH = ^AHC = 90 độ 

và ^HAC = ^HAK ( ^A chung ) 

=> \(\Delta\)AHC ~ \(\Delta\)AKH 

=> \(\frac{AH}{AK}=\frac{AC}{AH}\Rightarrow AH^2=AC.AK\)

d) Bạn kiểm tra lại đề nhé!

a: Xét ΔAHB vuông tại H và ΔCAB vuông tại A có

góc CBA chung

Do đó: ΔAHB\(\sim\)ΔCAB

Xét ΔAHB vuông tại H và ΔCHA vuông tại H có

\(\widehat{HAB}=\widehat{HCA}\)

Do đó: ΔAHB\(\sim\)ΔCHA

b: \(HC=\sqrt{10^2-6^2}=8\left(cm\right)\)

Xét ΔHAC có AD là phân giác

nên DH/HA=DC/AC

=>DH/3=DC/5

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{DH}{3}=\dfrac{DC}{5}=\dfrac{DH+DC}{3+5}=\dfrac{8}{8}=1\)

Do đó: DH=3cm; DC=5cm

c: Ta có: \(\widehat{BAD}+\widehat{CAD}=90^0\)

\(\widehat{BDA}+\widehat{HAD}=90^0\)

mà \(\widehat{CAD}=\widehat{HAD}\)

nên \(\widehat{BAD}=\widehat{BDA}\)

=>ΔBAD cân tại B

mà BK là đường phân giác

nên BK là đường cao

Xét ΔEFA vuông tại F và ΔEHB vuông tại H có

\(\widehat{FEA}=\widehat{HEB}\)

Do đó: ΔEFA\(\sim\)ΔEHB

29 tháng 3 2018

a)  Xét   \(\Delta HAC\) và     \(\Delta MAH\)có:

\(\widehat{AHC}=\widehat{AMH}=90^0\)

\(\widehat{HAC}\)      CHUNG

suy ra:   \(\Delta HAC~\Delta MAH\)

\(\Rightarrow\)\(\frac{AH}{AM}=\frac{AC}{AH}\)\(\Rightarrow\)\(AH^2=AM.AC\)

Giải :

a) Xét \(\Delta HBA\)và \(\Delta ABC\)có :

\(\widehat{BHA}=\widehat{BAC}=90^o\)

\(\widehat{B}\)chung

\(\Rightarrow\Delta HBA~\Delta ABC\left(g.g\right)\)

phần B đề sai sửa đề AH2 = HB . HC 

Áp dụng hệ thức cạnh trong \(\Delta\)vuông ta có :

\(AH^2=HB.HC\)( đpcm )

17 tháng 8 2019

chuyên toán thcsLớp 8 chưa học các HỆ THỨC LƯỢNG TRONG TAM GIÁC VUÔNG phải đi c.m chứ