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Giải bài 4 trang 66 SGK Toán 8 tập 2– Chân trời sáng tạo

Trong Hình 14, cho biết

﷽Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

Trong Hình 14, cho biết \(AB//CD\) a) Chứng minh rằng \(\Delta AEB\backsim\Delta DEC\). b) Tìm \(x\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Nếu một đường thẳng cắt phần kéo dài của hai cạnh của một tam giác và song song với cạnh còn lại thì nó tạo thành một tam giác mới đồng dạng với tam giác đã cho.

Lời giải chi tiết

a) Xét tam giác \(ABE\) có: \(AB//CD\) và \(C,D\) cắt \(BE;AE\) lần lượt tại \(C,D\). Do đó, \(\Delta AEB\backsim\Delta DEC\) (định lí) b) Vì \(\Delta AEB\backsim\Delta DEC\) nên \(\frac{{AE}}{{ED}} = \frac{{AB}}{{CD}}\) (các cặp cạnh tương ứng có cùng tỉ lệ). Thay số ta được: \(\frac{{x - 2}}{{10}} = \frac{3}{5} \Rightarrow x - 2 = \frac{{10.3}}{5} = 6 \Rightarrow x = 6 + 2 = 8\) Vậy \(x = 8\).

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