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Giải bài 6.9 trang 45 SGK Toán 8 - Cùng khám phá

Tính độ dài các cạnh của \(\Delta ABC\) trong Hình 6.27.
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Đề bài

Tính độ dài các cạnh của \(\Delta ABC\) trong Hình 6.27.

Phương pháp giải - Xem chi tiết

Áp dụng định lí Thales và tính chất của đường trung bình để tính độ dài các cạnh của tam giác \(ABC\) .

Lời giải chi tiết

Xét tam giác \(ABC\) , ta có: \(\widehat {ADE} = \widehat {ABC} = 90^\circ \) (mà hai góc này ở vị trí đồng vị)=> \(DE//BC\)Mà E là trung điểm của AC=> D là trung điểm cạnh AB (hệ quả của tính chất đường trung bình)=> DE là đường trung bình của tam giác \(ABC\)Ta có: \(\begin{array}{l}DE = \frac{1}{2}BC\\ = > BC = 2.4 = 8\end{array}\) \(AC = 5 + 5 = 10\) \(AB = 12\) 

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