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Giải bài 4.8 trang 83 SGK Toán 8 tập 1 - Kết nối tri thức

Cho tam giác ABC có trung tuyến AM.

🐎Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho tam giác ABC có trung tuyến AM. Lấy điểm D và E trên cạnh AB sao cho AD = DE = EB và D nằm giữa hai điểm A, E. a) Chứng minh DC // EM.

b) DC cắt AM tại I. Chứng minh I là trung điểm của AM.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a. Chứng minh EM là đường trung bình của tam giác BCD. b. Chứng minh DI là đường trung bình của tam giác AEM.

Lời giải chi tiết

a) Vì AM là đường trung tuyến của tam giác ABC nên M là trung điểm của BC.Ta có BE = DE và E ∈ BD nên E là trung điểm của BD.Xét tam giác BCD có E, M lần lượt là trung điểm của BD, BC nên EM là đường trung bình của tam giác BCD.Do đó DC // EM (tính chất đường trung bình).b) Ta có D là trung điểm của AE (vì AD = DE, D ∈ AE).Mà DI // EM (vì DC // EM).Do đó DI là đường trung bình của tam giác AEM.Suy ra I là trung điểm của AM.

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