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Giải bài 6.3 trang 42 SGK Toán 8 - Cùng khám phá

Tính độ dài \(x\) trong mỗi trường hợp ở hình 6.15
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Đề bài

Tính độ dài \(x\) trong mỗi trường hợp ở hình 6.15.

Phương pháp giải - Xem chi tiết

Dựa vào định lí Thales thuận để tìm độ dài x: Nếu một đường thẳng song song với một cạnh của tam giác và cắt hai cạnh còn lại thì nó định ra trên hai cạnh đó những đoạn thẳng tương ứng tỉ lệ.

Lời giải chi tiết

Xét tam giác \(ABC\), ta có:\(\begin{array}{l}\widehat {ABC} = 90^\circ \\\widehat {IJC} = 90^\circ \end{array}\)(mà hai góc này ở vị trí đồng vị)=> \(IJ//AB\)Dựa vào định lí Thales thuận ta có:\(\begin{array}{l}\frac{{IA}}{{AC}} = \frac{6}{{15}}\\\frac{{JB}}{{BC}} = \frac{x}{{13}}\\\frac{{IA}}{{AC}} = \frac{{JB}}{{AC}} \Leftrightarrow \frac{6}{{15}} = \frac{x}{{13}} \Rightarrow x = 5,2\end{array}\)Xét tam giác \(DEF\), ta có:\(GH//EF\)=> \(\frac{{GE}}{{DE}} = \frac{{HF}}{{DF}} \Leftrightarrow \frac{{4,5}}{7} = \frac{x}{{10}} \Rightarrow x = \frac{{45}}{7}\)Xét tam giác \(KMN\), ta có:\(PQ//MN\)=> \(\frac{{PM}}{{PK}} = \frac{{QN}}{{QK}} \Leftrightarrow \frac{x}{8} = \frac{2}{x} \Leftrightarrow x = 4\)

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