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Giải bài 13 trang 60 SGK Toán 8 tập 2– Chân trời sáng tạo

Tính độ dài

🔯Tổng 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

Tính độ dài \(x\) trong Hình 8

Phương pháp giải - Xem chi tiết

Định lí Thales 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 các đoạn thẳng tương ứng tỉ lệ.

Lời giải chi tiết

a) Xét tam giác \(ABC\) ta có \(MN//BC\), theo định lí Thales ta có:\(\frac{{AM}}{{MB}} = \frac{{AN}}{{NC}} \Leftrightarrow \frac{2}{4} = \frac{x}{7} \Rightarrow x = \frac{{2.7}}{4} = 3,5\)Vậy \(x = 3,5\).b) Vì \(\left\{ \begin{array}{l}AC \bot BD\\DE \bot BD\end{array} \right. \Rightarrow AC//DE\)Xét tam giác \(BDE\) ta có \(AC//DE\), theo định lí Thales ta có:\(\frac{{AB}}{{BD}} = \frac{{BC}}{{BE}} \Leftrightarrow \frac{3}{x} = \frac{5}{{3,5 + 5}} \Rightarrow x = \frac{{3.\left( {3,5 + 5} \right)}}{5} = 5,1\)Vậy \(x = 5,1\).c) Xét tam giác \(HIK\) ta có \(PQ//IK\), theo định lí Thales ta có:\(\frac{{HP}}{{HI}} = \frac{{HQ}}{{HK}} \Leftrightarrow \frac{x}{8} = \frac{{6,5}}{{6,5 + 3,5}} \Rightarrow x = \frac{{8.6,5}}{{\left( {6,5 + 3,5} \right)}} = 5,2\)Vậy \(x = 5,2\).

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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