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Bài 9 trang 179 Tài liệu dạy – học toán 6 tập 1

Giải bài tập Cho điểm M là trung điểm của đoạn thẳng AB. Trên tia đối của tia BA lấy điểm I bất kì. Chứng tỏ rằng IA + IB = 2IM.
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Đề bài

Cho điểm M là trung điểm của đoạn thẳng AB. Trên tia đối của tia BA lấy điểm I bất kì. Chứng tỏ rằng  IA + IB = 2IM.

Lời giải chi tiết

 

Ta có M là trung điểm của AB. Do đó M nằm giữa A và B, MA = MBTa có M \( \in \) tia BA (M nằm giữa A và B), và I \( \in \) tia đối của tia BA (đầu bài cho)Do đó hai tia BM, BI đối nhau. Nên B nằm giữa I và M \( \Rightarrow  IM = IB + MB\)Ta còn có M nằm giữa A và I nên \(IA = IM + MA\)Do đó:\(IA + IB = IM + MA + IB \)\(\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,= IM + MB + IB\)\(\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,= IM + (IB + MB) \)\(\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,= IM + IM = 2IM\)

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