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Giải Bài 9.1 trang 48 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Tam giác ABC có cạnh BC dài nhất. Chứng minh số đo góc A lớn hơn hoặc bằng 60

💦Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Tam giác ABC có cạnh BC dài nhất. Chứng minh số đo góc A lớn hơn hoặc bằng 600.

Phương pháp giải - Xem chi tiết

Áp dụng mối liên hệ giữa cạn và góc trong tam giác: Góc đối diện với cạnh lớn hơn là góc lớn hơn.

Lời giải chi tiết

Do cạnh BC dài nhất nên góc A lớn nhất (mối liên hệ giữa cạnh và góc trong tam giác) \( \Rightarrow \)\(\left\{ \begin{array}{l}\widehat A \ge \widehat B\\\widehat A \ge \widehat C\end{array} \right.\) Nếu \(\widehat A < {60^0} \Rightarrow \widehat B < {60^0};\widehat C < {60^0}\) \( \Rightarrow \widehat A + \widehat B + \widehat C < {60^0} + {60^0} + {60^0} = {180^0}\) (Vô lí) Vậy \(\widehat A \ge {60^0}\)

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