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Thử tại bạn trang 118(2) Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Ta đã biết trong một tam giác cân hai đường trung tuyến ứng với hai cạnh bên thì bằng nhau. Dựa vào tính chất đó, hãy chứng minh trong một tam giác đều ba đường trung tuyến ứng với ba cạnh thì bằng nhau (hình 60).
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Đề bài

Ta đã biết trong một tam giác cân hai đường trung tuyến ứng với hai cạnh bên thì bằng nhau. Dựa vào tính chất đó, hãy chứng minh trong một tam giác đều ba đường trung tuyến ứng với ba cạnh thì bằng nhau (hình 60).

 

Lời giải chi tiết

∆ABC đều (gt) => AB = AC = BC∆ABC cân tại A (AB = AC), BE và CF là hai đường trung tuyến (gt)=> BE = CF (1)∆ABC cân tại B (AB = BC), AD và CF là hai đường trung tuyến (gt)=> AD = CF (2)Từ (1) và (2) ta có AD = BE = CFVậy trung một tam giác đều ba đường trung tuyến ứng với ba cạnh thì bằng nhau.

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