Cho tam giác ABC Vuông tại A Có AB=3cm , AC=4cm , AH là đường cao , AD là phân giác Tính BC,BH,CH,BD,CD,HD. Giúp mik với ạ
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ΔABC vuông tại A
=>AB^2+AC^2=BC^2
=>BC=căn 3^2+4^2=5cm
ΔABC vuông tại A có AH là đường cao
nên AH*BC=AB*AC; BH*BC=BA^2; CH*CB=CA^2
=>AH=3*4/5=2,4cm; BH=3^2/5=1,8cm; CH=4^2/5=3,2cm
ΔABC có AD là phân giác
nên BD/AB=CD/AC
=>BD/3=CD/4=(BD+CD)/(3+4)=5/7
=>BD=15/7cm; CD=20/7cm
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
Xét tam giác \(ABC\) vuông tại \(A\) ta có:
\(A{B^2} + A{C^2} = B{C^2}\)
\( \Leftrightarrow {3^2} + {4^2} = B{C^2}\)
\( \Leftrightarrow B{C^2} = 25\)
\( \Rightarrow BC = 5cm\)
Ta có: \(BD + DC = BC \Rightarrow DC = BC - BD = 5 - BD\)
Vì \(AD\) là phân giác của góc \(BAC\) nên theo tính chất đường phân giác ta có:
\(\frac{{BD}}{{DC}} = \frac{{AB}}{{AC}} \Leftrightarrow \frac{{BD}}{{5 - BD}} = \frac{3}{4} \Leftrightarrow 4.BD = 3.\left( {5 - BD} \right) \Rightarrow 4.BD = 15 - 3.BD\)
\( \Leftrightarrow 4BD + 3BD = 15 \Leftrightarrow 7BD = 15 \Rightarrow BD = \frac{{15}}{7}\)
\( \Rightarrow DC = 5 - \frac{{15}}{7} = \frac{{20}}{7}\)
Vậy \(BC = 5cm;BD = \frac{{15}}{7}cm;DC = \frac{{20}}{7}cm\).
b) Diện tích tam giác \(ABC\) vuông tại \(A\) là:
\({S_{ABC}} = \frac{1}{2}AB.AC = \frac{1}{2}.4.3 = 6\left( {c{m^2}} \right)\)
Mặt khác \({S_{ABC}} = \frac{1}{2}.AH.BC = \frac{1}{2}.AH.5 = 6\)
\( \Rightarrow AH = \frac{{6.2}}{5} = 2,4cm\).
Xét tam giác \(AHB\) vuông tại \(H\) ta có:
\(A{H^2} + H{B^2} = A{B^2}\)
\( \Leftrightarrow H{B^2} = A{B^2} - A{H^2}\)
\( \Leftrightarrow H{B^2} = {3^2} - 2,{4^2}\)
\( \Leftrightarrow H{B^2} = 3,24\)
\( \Rightarrow HB = 1,8cm\)
\(HD = BD - BH = \frac{{15}}{7} - 1,8 = \frac{{12}}{7}cm\).
Xét tam giác \(AHD\) vuông tại \(H\) ta có:
\(A{H^2} + H{D^2} = A{D^2}\)
\( \Leftrightarrow A{D^2} = {\left( {\frac{{12}}{7}} \right)^2} + 2,{4^2}\)
\( \Leftrightarrow A{D^2} = \frac{{144}}{{49}} + \frac{{144}}{{25}}\)
\( \Rightarrow AD \approx 2,95cm\)
Vậy \(AH = 2,4cm;HD = \frac{{12}}{7}cm;AD = 2,95cm\).
![](https://rs.olm.vn/images/avt/0.png?1311)
BÀI 1:
a)
· Trong ∆ ABC, có: AB2= BC.BH
Hay BC= =
· Xét ∆ ABC vuông tại A, có:
AB2= BH2+AH2
↔AH2= AB2 – BH2
↔AH= =4 (cm)
b)
· Ta có: HC=BC-BH
àHC= 8.3 - 3= 5.3 (cm)
· Trong ∆ AHC, có:
·
Bài 1:
a) Áp dụng hệ thức lượng ta có:
\(AB^2=BH.BC\)
\(\Rightarrow\)\(BC=\frac{AB^2}{BH}\)
\(\Rightarrow\)\(BC=\frac{5^2}{3}=\frac{25}{3}\)
Áp dụng Pytago ta có:
\(AH^2+BH^2=AB^2\)
\(\Rightarrow\)\(AH^2=AB^2-BH^2\)
\(\Rightarrow\)\(AH^2=5^2-3^2=16\)
\(\Rightarrow\)\(AH=4\)
b) \(HC=BC-BH=\frac{25}{3}-3=\frac{16}{3}\)
Áp dụng hệ thức lượng ta có:
\(\frac{1}{HE^2}=\frac{1}{AH^2}+\frac{1}{HC^2}\)
\(\Leftrightarrow\)\(\frac{1}{HE^2}=\frac{1}{4^2}+\frac{1}{\left(\frac{16}{3}\right)^2}=\frac{25}{256}\)
\(\Rightarrow\)\(\frac{1}{HE}=\frac{5}{16}\)
\(\Rightarrow\)\(HE=\frac{16}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(AH^2=HB\cdot HC\)
\(\Leftrightarrow HC=\dfrac{4.8^2}{3.6}=6.4\left(cm\right)\)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB^2=36\\AC^2=64\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=6\left(cm\right)\\AC=8\left(cm\right)\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. áp dụng định lý pytago vào tam giác vuông ABC, ta có:
BC2=AB2+AC2
BC2= 32+42
BC2= 9+16
BC2=25
BC= 5 (cm)
Vì BD là phân giác
=> \(\dfrac{AD}{CD}\)=\(\dfrac{AB}{BC}\)
gọi AD là x, CD là 4-x
=> \(\dfrac{x}{4-x}\)=\(\dfrac{3}{5}\)
5x= 3.(4-x)
5x= 12-3x
5x+3x=12
8x=12
x= 1,5 (cm)
Vậy AD= 1,5 cm
b. Xét tam giác ABC và tam giác HBA:
góc A= góc H= 90o
góc B chung
=> tam giác ABC ~ tam giác HBA
c. Vì tam giác ABC ~ tam giác HBA (cmt)
=> \(\dfrac{AB}{HB}\)=\(\dfrac{BC}{AB}\)
=> AB2=BC.HB
![](https://rs.olm.vn/images/avt/0.png?1311)
3:
\(BC=\sqrt{12^2+16^2}=20\left(cm\right)\)
HB=12^2/20=7,2cm
=>HC=20-7,2=12,8cm
\(AD=\dfrac{2\cdot12\cdot16}{12+16}\cdot cos45=\dfrac{48\sqrt{2}}{7}\)
\(HD=\sqrt{AD^2-AH^2}=\dfrac{48}{35}\left(cm\right)\)
Lời giải:
Áp dụng định lý Pitago:
$BC=\sqrt{AB^2+AC^2}=\sqrt{3^2+4^2}=5$ (cm)
Áp dụng hệ thức lượng trong tam giác vuông:
$BH=\frac{AB^2}{BC}=\frac{3^2}{5}=\frac{9}{5}=1,8$ (cm)
$CH=BC-BH=5-1,8=3,2$ (cm)
$\frac{BD}{CD}=\frac{AB}{AC}=\frac{3}{4}$
$\Rightarrow \frac{BD}{BD+CD}=\frac{3}{7}$
Hay $\frac{BD}{BC}=\frac{3}{7}\Rightarrow BD=\frac{3}{7}.BC=\frac{3}{7}.5=\frac{15}{7}$ (cm)
$CD=BC-BD=5-\frac{15}{7}=\frac{20}{7}$ (cm)
$HD=BD-BH=\frac{15}{7}-1,8=\frac{12}{35}$ (cm)
Hình vẽ:
![](data:image/png;base64,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)