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Giải bài 6 trang 66 SGK Toán 8 tập 2– Chân trời sáng tạo

Người ta ứng dụng hai tam giác đồng dạng để đo

🌊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

Người ta ứng dụng hai tam giác đồng dạng để đo khoảng cách \(BC\) ở hai điểm không thể đến được (hình 15). Biết \(DE//BC\). a) Chứng minh rằng \(\Delta ADE\backsim\Delta ABC\). b) Tính khoảng cách \(BC\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Nếu một đường thẳng cắt hai cạnh của một tam giác và song song với cạnh còn lại thì nó tạo thành một tam giác mới đồng dạng với tam giác đã cho.

- Nếu \(\Delta A'B'C'\backsim\Delta ABC\) theo tỉ số \(k\) ไthì \(\left\{ \begin{array}{l}\widehat A = \widehat {A'};\widehat B = \widehat {B'};\widehat C = \widehat {C'}\\\frac{{A'B'}}{{AB}} = \frac{{A'C'}}{{AC}} = \frac{{B'C'}}{{BC}} = k\end{array} \right.\)

Lời giải chi tiết

a) Xét tam giác \(ABC\) ta có: \(DE//BC\) và \(D,E\) cắt \(AB;AC\) tại \(D;E\). Do đó, \(\Delta ADE\backsim\Delta ABC\) (định lí) b) Vì \(\Delta ADE\backsim\Delta ABC\) nên \(\frac{{AD}}{{AB}} = \frac{{DE}}{{BC}}\) (cách cặp cạnh tương ứng có cùng tỉ lệ). Thay số, \(\frac{{16}}{{30}} = \frac{{22}}{{BC}} \Rightarrow BC = \frac{{22.30}}{{16}} = 41,25\) Vậy \(BC = 41,25m\).

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