Cho tam giác ABC vuông tại A, vẽ đường cao AH biết AB=6cm, AC=8cm.
a.vẽ hình và ghi chú
b. Tính BC
c. tính BH
d. tính HC
e. tính AH
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a, AB = 7,5cm, AC = 10cm, BC = 12,5cm, HC = 8cm
b, AH = 3 3 cm; P A B C = 18 + 6 3 c m ; P A B H = 9 + 3 3 c m ; P A C H = 9 + 9 3 c m
a.
\(BC^{2} = AB^{2} + AC^{2}\)
⇔ \(BC^{2} = 6^{2} + 8^{2}\)
⇔ \(BC = 10 cm\)
b.
\(\dfrac{1}{AH^{2}} = \dfrac{1}{AB^{2}} + \dfrac{1}{AC^{2}}\)
⇔ \(\dfrac{1}{AH^{2}} = \dfrac{1}{6^{2}} + \dfrac{1}{8^{2}}\)
⇔ \(AH = 4,8 cm\)
a)
Xét \(\Delta ABC\)và \(\Delta HBA\) có:
\(\widehat{A}=\widehat{H}=90^o\)
\(\widehat{B}\)là góc chung
\(\Rightarrow\Delta ABC\)đồng dạng với \(\Delta HBA\)
\(\RightarrowĐpcm\)
b)
Xét \(\Delta ABC\) và \(\Delta HAC\) có:
\(\widehat{A}=\widehat{H}=90^o\)
\(\widehat{C}\)là góc chung
\(\Rightarrow\Delta ABC\)đồng dạng với \(\Delta HAC\)
\(\Rightarrow\Delta HBA\)đồng dạng với \(\Delta HAC\) (bắc cầu)
Vì \(\Delta HBA\)đồng dạng với \(\Delta HAC\)
\(\Rightarrow\frac{AH}{HC}=\frac{HB}{AH}\Rightarrow AH^2=HB.HC\Rightarrowđpcm\)
a) Ta có BE là phân giác của ∠ABC (gt)
⇒ ∠B1 = ∠B2
Do đó hai tam giác vuông:
b) Ta có:
(định lý Pitago)
Xét hai tam giác vuông AHB và CAB có góc B chung nên :
a) Áp dụng định lí Pytago vào ΔABC vuông tại A, ta được:
\(BC^2=AB^2+AC^2\)
\(\Leftrightarrow BC^2=6^2+8^2=100\)
hay BC=10(cm)
Vậy:BC=10cm
Lời giải:
a. Áp dụng định lý Pitago: $BC=\sqrt{AB^2+AC^2}=\sqrt{6^2+8^2}=10$ (cm)
b. Áp dụng HTL trong tam giác vuông:
$AB^2=BH.BC\Rightarrow BH=\frac{AB^2}{BC}=\frac{6^2}{10}=3,6$ (cm)
c.
$CH=BC-BH=10-3,6=6,4$ (cm)
d. Áp dụng HTL trong tam giác vuông:
$AH^2=BH.CH=3,6.6,4=23,04$
$\Rightarrow AH=\sqrt{23,04}=4,8$ (cm)
Hình vẽ:
![](data:image/png;base64,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)