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Giải Bài 4 trang 60 sách bài tập toán 7 - Chân trời sáng tạo

Cho tam giác ABC có ba trung tuyến AM, BN, CP đồng quy tại G. Chứng minh: \(GA + GB + GC = \frac{2}{3}\left( {AM + BN + CP} \right)\)

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Đề bài

Cho tam giác ABC có ba trung tuyến AM, BN, CP đồng quy tại G. Chứng minh: \(GA + GB + GC = \frac{2}{3}\left( {AM + BN + CP} \right)\)

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Lời giải chi tiết

Ta có G là trọng tâm tam giác ANC, do đó ta có:\(GA = \frac{2}{3}AM;GB = \frac{2}{3}BN;GC = \frac{2}{3}CP\)Suy ra: \(GA + GB + GC = \frac{2}{3}\left( {AM + BN + CP} \right)\)

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