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Giải bài 9.22 trang 76 SGK Toán 7 tập 2 - Kết nối tri thức

Cho tam giác ABC có các đường trung tuyến BM và CN cắt nhau tại G. Biết góc GBC lớn hơn góc GCB. Hãy so sánh BM và CN.

ꦆTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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Đề bài

Cho tam giác ABC có các đường trung tuyến BM và CN cắt nhau tại G. Biết góc GBC lớn hơn góc GCB. Hãy so sánh BM và CN.

Phương pháp giải - Xem chi tiết

Dựa vào quan hệ giữa góc và cạnh đối diện trong tam giác GBC để so sánh BG và CG. Sử dụng định lí về sự đồng quy của ba đường trung tuyến trong tam giác để so sánh BM và CN.

Lời giải chi tiết

Xét tam giác BGC có \( \widehat {GBC} > \widehat {GCB} \) suy ra CG > BG (1) Hai đường trung tuyến BM và CN cắt nhau tại G nên theo định lí về sự đồng quy của ba đường trung tuyến trong tam giác ta có: \( CG = \frac{2}{3}CN; BG = \frac{2}{3}BM\) (2) Từ (1) và (2) suy ra CN > BM.

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