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Giải bài 4 trang 71 SGK Toán 8 tập 2– Chân trời sáng tạo

Xét xem cặp tam giác nào trong Hình 16a,16b đồng dạng?

🦂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

Xét xem cặp tam giác nào trong Hình 16a,16b đồng dạng?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Nếu hai cạnh của tam giác này tỉ lệ với hai cạnh của tam giác kia và hai góc tạo bởi các cặp cạnh đó bằng nhau thì hai tam giác đó đồng dạng.

Lời giải chi tiết

- Xét Hình 16a Ta có: \(\frac{{DE}}{{AB}} = \frac{6}{{12}} = \frac{1}{2};\frac{{DF}}{{AC}} = \frac{9}{{18}} = \frac{1}{2}\) Xét tam giác \(DEF\) và tam giác \(ABC\) ta có: \(\frac{{DE}}{{AB}} = \frac{{DF}}{{AC}} = \frac{1}{2}\) \(\widehat {BAC} = \widehat {EDF} = 120^\circ \) Do đó, \(\Delta DEF\backsim\Delta ABC\) (c.g.c) - Xét Hình 16b Ta có: \(\frac{{CE}}{{NP}} = \frac{4}{8} = \frac{1}{2};\frac{{DE}}{{MP}} = \frac{5}{{10}} = \frac{1}{2}\) Tuy nhiên, quan sát hình vẽ ta có thể thấy góc tạo bởi cạnh \(MP;NP\) là \(\widehat P\) và góc tạo bởi cạnh \(DE;CE\) là góc \(\widehat E\). Ta thấy hai góc này không bằng nhau nên chúng không đồng dạng.

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