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Giải bài 3 trang 69 SGK Toán 8 – Cánh diều

Quan sát Hình 43 và chứng minh

🍰Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Quan sát Hình 43൩ và chứng minh \(\frac{{DB}}{{DC}}:\frac{{EB}}{{EG}} = \frac{{AG}}{{AC}}\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Sử dụng tính chất đường phân giác để chứng minh yêu cầu bài toán.

Lời giải chi tiết

Xét tam giác ABC với đường phân giác AD ta có: \(\frac{{DB}}{{DC}} = \frac{{AB}}{{AC}}\) (Tính chất đường phân giác) Xét tam giác ABG với đường phân giác AE ta có: \(\frac{{EB}}{{EG}} = \frac{{AB}}{{AG}}\)(Tính chất đường phân giác) \( \Rightarrow \frac{{DB}}{{DC}}:\frac{{EB}}{{EG}} = \frac{{AB}}{{AC}}:\frac{{AB}}{{AG}} = \frac{{AG}}{{AC}}\) (đpcm)

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