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Bài tập 3 trang 96 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Cho tam giác ABC vuông tại A
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Đề bài

Cho tam giác ABC vuông tại A có \(\widehat B = {45^o}\) a) So sánh các cạnh của tam giác ABC. b) Lấy điểm K bất kì thuộc đoạn thẳng AC. So sánh độ dài các cạnh BK, BC.

Lời giải chi tiết

a) ∆ABC vuông tại A (gt) \( \Rightarrow \widehat B + \widehat C = 90^\circ\)Mà \(\widehat B > 45^\circ  \Rightarrow \widehat C < 45^\circ\)Do đó \(\widehat C < \widehat B < \widehat A\)∆ABC có \(\widehat C < \widehat B < \widehat A\) => AB < AC < BC (định lí cạnh đối diện với góc lớn hơn)b) Ta có \(\widehat {BKC} > \widehat {BAK}(\widehat {BKC}\) là góc ngoài của tam giác ABK)∆BKC có \(\widehat {BKC} > 90^\circ  \Rightarrow \widehat {BKC}\) là góc lớn nhất trong ba góc=> BC là cạnh lớn nhất trong ba cạnh.Vậy BC > BK.

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