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Giải bài 6.12 trang 47 SGK Toán 8 - Cùng khám phá

Cho tứ giác \(ABCD\) có \(AB = AD\) . Đường phân giác của góc \(BAC\) cắt \(BC\) tại
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Đề bài

Cho tứ giác \(ABCD\) có \(AB = AD\) . Đường phân giác của góc \(BAC\) cắt \(BC\) tại điểm \(E\) đường phân giác của góc \(CAD\) cắt \(CD\) tại \(F\) . Chứng minh rằng \({\rm{EF}}\) song song với \(BD.\) 

Phương pháp giải - Xem chi tiết

Dựa vào tính chất đường phân giác của một tam giác: Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn ấy.

Lời giải chi tiết

Ta có: \(\frac{{DF}}{{FC}} = \frac{{AD}}{{AC}}\) (AF là đường phân giác) \(\frac{{CE}}{{EB}} = \frac{{AC}}{{AB}}\) (AE là đường phân giác)=> \(\frac{{DF}}{{FC}} = \frac{{BE}}{{EC}}\)Áp dụng định lý thales suy ra \(BD//EF\) 

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