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Bài tập 13 trang 122 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Cho tam giác ABC cân tại A. Tia phân giác của góc B và C gặp nhau tại M. Tia AM cắt BC tại H. Chứng minh rằng H là trung điểm của BC.
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Đề bài

Cho tam giác ABC cân tại A. Tia phân giác của góc B và C gặp nhau tại M. Tia AM cắt BC tại H. Chứng minh rằng H là trung điểm của BC.

Lời giải chi tiết

 

∆ABC có M là giao điểm của hai đường phân giác xuất phát từ B và C (gt)Nên theo định lý về ba đường phân giác của tam giác, ta có:M là điểm cách đều ba cạnh của tam giác ABC.=> AM là tia phân giác của \(\widehat {BAC}\)∆ABC cân tại A có AH là đường phân giác=> AH cũng là đường trung tuyếnVậy H là trung điểm của BC.

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