ba lớp 7A 7B 7C tham gia phong trào kế hoạch nhỏ thu gom rác nhà trường do phát động số giấy thu gom được của 3 lớp 7a 7b 7c lần lượt tỉ lệ 3;5;6.biết số giấy thu gom được của lớp 7b hơn số giấy thu gom được của lớp 7a là 18kg tính số kg giấy thu gom được của mỗi lớ
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1.It's about 25km from my house to my grandparents' house
2.I used to ride a small bike in the yard outside the flat
3.The used to be a bus station in the city center but it was moved to the suburds
4.Children must learn about road side before they are allowed to ride a bike on the road
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a) xét tam giác ABC zà tam giác ACD có
AB=AD(gt)
AC chung
góc BAC= góc CAD =90 độ
=> 2 tam giác trên = nhau
=>\(\hept{\begin{cases}\widehat{DCA}=\widehat{ACB}\\DC=BC\end{cases}}\)
=>\(\hept{\begin{cases}\widehat{DCA}+\widehat{ACB}=30^0+30^0=60\\\Delta DBC\left(cân\right)\end{cases}}\)
=> \(\Delta DBC\)đều
b) ta có tam giác BAC cân
tam giác BAD đều
=>\(\hept{\begin{cases}AC=AB\\BD=BC=DC\end{cases}}\)
=> \(\hept{\begin{cases}AC=AB\\\frac{1}{2}BD=\frac{1}{2}BC=\frac{1}{2}DC\end{cases}}\)
=> \(\hept{\begin{cases}AC=AB\\AB=AD=\frac{1}{2}BC=\frac{1}{2}DC\end{cases}}\)
=>\(AD=\frac{1}{2}BC=>BC=2AD\)
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A B C H
Áp dụng định lý Pythagoras ta có:
\(AH^2+BH^2=AC^2\Rightarrow AC^2-BH^2=AH^2\)
\(AH^2+HC^2=AC^2\Leftrightarrow AC^2-HC^2=AH^2\)
Khi đó:
\(AC^2-BH^2=AC^2-HC^2\)
\(\Rightarrow AC^2+HC^2=AC^2+BH^2\)
=> ĐPCM
A B C H
Áp dụng định lí pitago cho \(\Delta\)AHC vuông tại H ta có:
\(AC^2=AH^2+CH^2\)
=> \(BH^2+AC^2=BH^2+AH^2+CH^2\)(1)
Áp dụng định lí pitago cho \(\Delta\)ABH vuông tại H ta có:
\(AB^2=AH^2+BH^2\)(2)
Từ (1); (2) => \(BH^2+AC^2=AB^2+CH^2\)( đpcm)
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Gọi số kg giấy của 3 lớp A; B ; C lần lượt là x; y; z ( >0 ; kg)
Theo đề baì số kg giấy của 3 lớp A;B:C lần lượt tỉ lệ với: 3;5 ; 6
=> \(\frac{x}{3}=\frac{y}{5}=\frac{z}{6}\)
Mặt khác số kg giấy của 7B nhiều hơn 7A là 18 kg
=> y - x = 18
Áp dụng dãy tỉ số bằng nhau ta có:
\(\frac{x}{3}=\frac{y}{5}=\frac{z}{6}=\frac{y-x}{5-3}=\frac{18}{2}=9\)
=> \(\hept{\begin{cases}\frac{x}{3}=9\\\frac{y}{5}=9\\\frac{z}{6}=9\end{cases}}\Leftrightarrow\hept{\begin{cases}x=27\\y=45\\z=54\end{cases}}\)( tm )
Kết luận: Số kg giấy thu gom được của 3 lớp A; B: C lần lượt là: 27kg ; 45kg ; 54 kg.