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Giải bài 61 trang 83 sách bài tập toán 8 – Cánh diều

Cho tam giác \(ABC\) có \(DE//BC\) (Hình 55). Khẳng định nào dưới đây đúng?

🏅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 tam giác \(ABC\) có \(DE//BC\) (Hình 55). Khẳng định nào dưới đây đúng?

A. \(\frac{AD}{AB}+\frac{CA}{CE}=1\)
B. \(\frac{AB}{AD}+\frac{CE}{CA}=1\)
C. \(\frac{AD}{AB}+\frac{CE}{CA}=1\)
D. \(\frac{AC}{AB}+\frac{CE}{CA}=1\)

Phương pháp giải - Xem chi tiết

Dựa vào định lí Thales: Nếu một đường thẳng song song với một cạnh của tam giác và cắt hai cạnh còn lại thì nó định ra trên hai cạnh đó những đoạn thẳng tương ứng tỉ lệ.

Lời giải chi tiết

Chọn đáp án CTam giác \(ABC\)AB có \(DE//BC\) nên theo định lí Thales ta có:\(\frac{AD}{AB}=\frac{AE}{CA}=\frac{CA-CE}{CA}=1-\frac{CE}{CA}\)\(=>\frac{AD}{AB}+\frac{CE}{CA}=1\).

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