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Giải bài 2 trang 49 SGK Toán 8 tập 2– Chân trời sáng tạo

Tìm

𒐪Tổng 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

Tìm \(x\) trong Hình 20.

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

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 \(ABC\) có \(MN//BC\) nên theo định lí Thales ta có: \(\frac{{AM}}{{MB}} = \frac{{AN}}{{NC}} \Rightarrow \frac{x}{2} = \frac{{4,5}}{3}\). Do đó, \(x = \frac{{4,5.2}}{3} = 3\). Vậy \(x = 3\). b) Ta có: \(CD = AC + AD = 3 + 6 = 9\) Xét tam giác \(CDE\) có \(AB//DE\) nên theo định lí Thales ta có: \(\frac{{AC}}{{CD}} = \frac{{BC}}{{CE}} \Rightarrow \frac{3}{9} = \frac{{2,4}}{x}\). Do đó, \(x = \frac{{9.2,4}}{3} = 7,2\). Vậy \(x = 7,2\). c) Vì \(\left\{ \begin{array}{l}DE \bot PM\\MN \bot PM\end{array} \right. \Rightarrow DE//MN\) (quan hệ từ vuông góc đến song song). \(PE + EN = 3,9 + 2,6 = 6,5\) Xét tam giác \(PMN\) có \(DE//MN\) nên theo định lí Thales ta có: \(\frac{{DM}}{{MP}} = \frac{{NE}}{{NP}} \Rightarrow \frac{x}{5} = \frac{{2,6}}{{6,5}}\). Do đó, \(x = \frac{{2,6.5}}{{6,5}} = 2\). Vậy \(x = 2\).

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

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