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Giải bài 1 trang 53 SGK Toán 8 tập 2– Chân trời sáng tạo

Cho

ಌTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho \(MN\) là đường trung bình của mỗi tam giác \(ABC\) trong Hình 9. Hãy tìm giá trị \(x\) trong mỗi hình.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Đường trung bình của tam giác thì song song với cạnh thứ ba và bằng nửa cạnh ấy.

Lời giải chi tiết

- Hình a: Vì \(MN\) là đường trung bình của tam giác \(ABC\) nên theo tính chất đường trung bình ta có: \(\left\{ \begin{array}{l}MN//BC\\MN = \frac{1}{2}BC\end{array} \right. \Rightarrow MN = \frac{1}{2}x \Leftrightarrow 6 = \frac{1}{2}x \Leftrightarrow x = 6:\frac{1}{2} = 12\) - Hình b: Vì \(MN\) là đường trung bình của tam giác \(ABC\) nên theo tính chất đường trung bình ta có: \(\left\{ \begin{array}{l}MN//BC\\MN = \frac{1}{2}BC\end{array} \right. \Rightarrow MN = \frac{1}{2}\left( {2x + 3} \right) \Leftrightarrow 7 = \frac{1}{2}\left( {2x + 3} \right) \Leftrightarrow \left( {2x + 3} \right) = 7:\frac{1}{2} = 14\) \( \Rightarrow 2x = 14 - 3 \Leftrightarrow 2x = 11 \Leftrightarrow x = 5,5\). - Hình c Vì \(MN\) là đường trung bình của tam giác \(ABC\) nên theo tính chất đường trung bình ta có: \(\left\{ \begin{array}{l}MN//BC\\MN = \frac{1}{2}BC\end{array} \right. \Rightarrow MN = \frac{1}{2}.58 \Leftrightarrow \left( {5x - 1} \right) = \frac{1}{2}.58\) \( \Leftrightarrow \left( {5x - 1} \right) = 29 \Leftrightarrow 5x = 30 \Leftrightarrow x = 30:5 \Leftrightarrow x = 6\).

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