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Cho tam giác ABC, trên tia đối của tia AB lấy D sao cho AD = AB

cho tam giác ABC ,trên tia đối của tia AB lấy D sao cho AD = AB.Lấy G thuộc AC sao cho AG = 1/3AC.Tia DG cắt BC ở E.Qua E vẽ đường thẳng song song với BD;Qua D vẽ đường thẳng song song với BC,2 đường này cắt nhau ở F.Gọi M là giao điểm của EF và CD.
CMR:M là trung điểm của đoạn thẳng DC
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
Ta có:
- Vì AD = AB nên tam giác ABD đều.
- Ta có AG = 1/3AC = 1/3(AB + BC) = 1/3(AD + DC) = 1/3(AB + DC) = 1/3(AB + 2BM) = 1/3(AB + 2DM) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3(AD + DC) = 1/3AC.
=> AG = 1/3AC = 1/3(AD + DC) = 1/3(AD + 2DM) = 1/3

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