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Giải Bài 9.3 trang 48 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Hãy giải thích tại sao trong tam giác vuông, cạnh huyền dài nhất và trong tam giác tù, cạnh đối diện với góc tù là cạnh lớn nhất

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

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Đề bài

Hãy giải thích tại sao trong tam giác vuông, cạnh huyền dài nhất và trong tam giác tù, cạnh đối diện với góc tù là cạnh lớn nhất

Phương pháp giải - Xem chi tiết

Trong tam giác vuông, góc vuông là góc lớn nhất do hai góc còn lại đều là góc nhọn, nên cạnh đối điện với nó là cạnh huyền dài nhất Tương tự, trong tam giác tù có một góc tù thì 2 góc còn lại đều nhọn nên góc tù là góc lớn nhất; vậy cạnh đối diện góc tù là cạnh lớn nhất.

Lời giải chi tiết

-Xét tam giác ABC vuông tại B:

\(\widehat B = {90^0} \Rightarrow \left\{ \begin{array}{l}\widehat B > \widehat A\\\widehat B > \widehat C\end{array} \right.\)Mà cạnh đối diện với góc vuông là ACVậy cạnh huyền AC lớn nhất (mối liên hệ giữa cạnh và góc trong tam giác)-Xét tam giác tù ABC với góc A là góc tù:

\( \Rightarrow \widehat B,\widehat C\) là góc nhọn.\( \Rightarrow \widehat A\)là góc lớn nhất.Cạnh đối diện với góc A là cạnh BC\( \Rightarrow BC\)là cạnh lớn nhất (mối liên hệ giữa cạnh và góc trong tam giác)

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