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Giải bài 5 trang 73 SGK Toán 8 – Cánh diều

Cho tam giác ABC (Hình 55), các điểm M, N thuộc cạnh AB thỏa mãn

𝄹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 (Hình 55)💦, các điểm M, N thuộc cạnh AB thỏa mãn \(AM = MN = NB\), các điểm P, Q thuộc cạnh AC thỏa mãn \(AP = PQ = QC\). Tam giác AMP đồng dạng với những tam giác nào?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Sử dụng định lý về cặp tam giác đồng dạng nhận được từ định lý Thales để tìm ra các cặp tam giác đồng dạng.

Lời giải chi tiết

Vì \(AM = MN = NB\) và \(AP = PQ = QC\) nên M và P lần lượt là trung điểm của AN và AQ. Khi đó MP là đường trung bình của tam giác ANQ. \(\Rightarrow MP//NQ\) \(\Rightarrow \Delta AMP \backsim \Delta ANQ\) (theo định lí) \(\Rightarrow \widehat {AMP} = \widehat {ANQ}\) Ta có: \(\frac{{AM}}{{AB}} = \frac{{AP}}{{AC}} = \frac{1}{3} \Rightarrow MP//BC\) (Định lý Thales đảo) \( \Rightarrow \Delta AMP \backsim \Delta ABC\).

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