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Nguyễn Thị Giang
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Trần Hà Nhi
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nguyễn đức tín
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nguyễn đức tín
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aloha cong
9 tháng 1 2017 lúc 21:41

bài này có đúng k z bạn?

Nguyễn Đức Anh
20 tháng 2 2020 lúc 19:18

đề bài sai r

Khách vãng lai đã xóa
Phạm Nguyễn Thúy Vy
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Nguyễn Hoàng Minh
30 tháng 9 2021 lúc 15:55

Tam giác ABD vuông tại D có \(\cos\widehat{A}=\cos60^0=\dfrac{AD}{AB}=\dfrac{1}{2}\)

Tam giác AEC vuông tại E có \(\cos\widehat{A}=\cos60^0=\dfrac{AE}{AC}=\dfrac{1}{2}\)

Ta có \(\left\{{}\begin{matrix}\dfrac{AD}{AB}=\dfrac{AE}{AC}\left(=\dfrac{1}{2}\right)\\\widehat{A}.chung\end{matrix}\right.\Rightarrow\Delta ADE\sim\Delta ABC\left(c.g.c\right)\)

\(\Rightarrow\dfrac{DE}{BC}=\dfrac{AD}{AB}=\dfrac{1}{2}\\ \Rightarrow2DE=BC\)

Nguyễn Duy Khang
30 tháng 9 2021 lúc 16:56

Bạn tự vẽ hình

Đặt \(AB=x\)

Xét \(\Delta DAB\) vuông tại D, ta có:

\(\cos A=\dfrac{AD}{AB}\) (tỉ số lượng giác)

\(\Rightarrow AD=AB.\cos A=x.\cos60^o=0,5x\)

Xét \(\Delta ADB\) và \(\Delta AEC\), ta có:

\(\left\{{}\begin{matrix}\widehat{A}chung\\\widehat{ABD}=\widehat{ACE\left(2gocphunhau\right)}\end{matrix}\right.\) 
\(\Rightarrow\Delta ADB\sim\Delta AEC\left(g.g\right)\)

Xét \(\Delta ABC\) và \(\Delta ADE\), ta có:

\(\left\{{}\begin{matrix}\widehat{A}chung\\\dfrac{AB}{AC}=\dfrac{AD}{AE}\left(\Delta ABD\sim\Delta ADE\right)\end{matrix}\right.\)

\(\Rightarrow\Delta ABC\sim\Delta ADE\left(c.g.c\right)\\ \Rightarrow\dfrac{AB}{AD}=\dfrac{BC}{DE}\\ \Rightarrow\dfrac{x}{0,5x}=\dfrac{BC}{DE}\\ \Rightarrow BC=\dfrac{DE.x}{0,5x}=2DE\)

 

 

Laura Lê
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Lê Hoàng Ân
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