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Giải bài 7 trang 42 sách bài tập toán 8 - Chân trời sáng tạo tập 2

Cho tam giác ABC và điểm M trên cạnh AB sao cho \(\frac{{AM}}{{MB}} = \frac{3}{2}\). Kẻ MN//BC \(\left( {N \in AC} \right)\). Biết \(BC = 6cm\), tính độ dài MN.

🅺Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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Đề bài

Cho tam giác ABC và điểm M trên cạnh AB sao cho \(\frac{{AM}}{{MB}} = \frac{3}{2}\). Kẻ MN//BC \(\left( {N \in AC} \right)\). Biết \(BC = 6cm\), tính độ dài MN.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về hệ quả định lí Thalès trong tam giác để tính: Nếu một đường thẳng cắt hai cạnh của một tam giác song song với cạnh thứ ba thì tạo ra một tam giác mới có ba cạnh tương ứng tỉ lệ với ba cạnh của tam giác đã cho. 

Lời giải chi tiết

Vì \(\frac{{AM}}{{MB}} = \frac{3}{2}\) nên \(AM = \frac{3}{5}AB\)Tam giác ABC có: MN//BC nên theo hệ quả của định lí Thalès ta có:\(\frac{{MN}}{{BC}} = \frac{{AM}}{{AB}}\) nên \(\frac{{MN}}{6} = \frac{3}{5}\), suy ra: \(MN = \frac{{18}}{5}\left( {cm} \right)\)

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