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Giải bài 4 trang 94 SGK Toán 8 – Cánh diều

Cho tứ giác ABCD. Tia phân giác của các góc BAD và BCD cắt nhau tại điểm I

🌞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

Cho tứ giác ABCD. Tia phân giác của các góc BAD và BCD cắt nhau tại điểm I. Biết I thuộc đoạn thẳng BD (Hình 103). Chứng minh \(AB.CD = AD.BC\).

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Dựa vào tính chất đường phân giác để suy ra các tỉ lệ tương ứng.

Lời giải chi tiết

Vì AI là đường phân giác của góc DAB nên \(\frac{{ID}}{{IB}} = \frac{{AD}}{{AB}}\) (Tính chất đường phân giác) Vì CI là đường phân giác của góc BCD nên \(\frac{{ID}}{{IB}} = \frac{{CD}}{{CB}}\) (Tính chất đường phân giác) \( \Rightarrow \frac{{AD}}{{AB}} = \frac{{CD}}{{CB}} \Rightarrow AB.CD = AD.BC\)

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