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Giải bài 4.3 trang 80 SGK Toán 8 tập 1 - Kết nối tri thức

Cho ∆ABC, từ điểm D trên cạnh BC,

🐎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 ∆ABC, từ điểm D trên cạnh BC, kẻ đường thẳng song song với AB cắt AC tại F và kẻ đường thẳng song song với AC cắt AB tại E. Chứng minh rằng: \(\dfrac{{A{\rm{E}}}}{{AB}} + \dfrac{{AF}}{{AC}} = 1\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng định lí Thalès trong tam giác ABC, ta có các tỉ lệ thức. Áp dụng dãy tỉ số bằng nhau ta được đpcm.

Lời giải chi tiết

Áp dụng định lí Thalès, ta có: • Vì DE // AC nên \(\dfrac{{A{\rm{E}}}}{{AB}} = \dfrac{{C{\rm{D}}}}{{BC}}\) • Vì DF // AB nên \(\dfrac{{AF}}{{AC}} = \dfrac{{B{\rm{D}}}}{{BC}}\) Khi đó, \(\dfrac{{A{\rm{E}}}}{{AB}} + \dfrac{{AF}}{{AC}} = \dfrac{{C{\rm{D}}}}{{BC}} + \dfrac{{B{\rm{D}}}}{{BC}} = 1\) (đpcm).

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