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Bài tập 5 trang 120 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Cho tam giác nhọn ABC. Trên tia đối của tia AB lấy điểm D sao AD = AB.
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Đề bài

Cho tam giác nhọn ABC. Trên tia đối của tia AB lấy điểm D sao AD = AB. Trên cạnh AC lấy điểm E sao cho \(AE = {1 \over 3}AC\) . a) Chứng minh E là trọng tâm tam giác BCD. b) Gọi M là trung điểm của DC. Chứng minh ba điểm B, M, E thẳng hàng.

Lời giải chi tiết

 

a) Xét ∆BCD có: CA là đường trung tuyến (AD = AB)E trên đoạn thẳng CA\(CE = {2 \over 3}CA\) (vì\(AE = {1 \over 3}AC\))Nên E là trọng tâm của tam giác BCD.b) ∆BDC có: BM là đường trung tuyến (M là trung điểm của DC)E là trọng tâm (câu a)Do đó BM đi qua E. Vậy B, M, E thẳng hàng.

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