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Giải bài 1 trang 66 SGK Toán 7 tập 2 - Chân trời sáng tạo

a) So sánh các góc của tam giác ABC có AB = 4 cm, BC = 7 cm, AC = 6 cm. b)So sánh các cạnh của tam giác ABC có

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Đề bài

a) So sánh các góc của tam giác ABC có AB = 4 cm, BC = 7 cm, AC = 6 cm. b) So sánh các cạnh của tam giác ABC có \(\widehat A\)\( = {50^o}\),\(\widehat C\)\( = {50^o}\)

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Phương pháp giải - Xem chi tiết

- Sử dụng định lí về góc đối diện cạnh trong tam giác - Sử dụng tính chất tam giác cân và tính góc còn lại của tam giác để so sánh độ dài các cạnh

Lời giải chi tiết

a) Theo đề bài ta có AB = 4cm, BC = 7cm, AC = 6cmCó góc đối diện với cạnh AB là góc C, góc A đối diện với cạnh BC, góc B đối diện với cạnh ACTheo định lí về góc đối diện với cạnh lớn hơn thì lớn hơn ta có :\( \Rightarrow \widehat A > \widehat B > \widehat C\)b)Vì \(\widehat{A}=\widehat{C}\) nên tam giác ABC cân tại B\( \Rightarrow BA = BC\)Áp dụng định lí tổng 3 góc trong tam giác ABC, có:\( \Rightarrow \widehat B = {180^o} - {100^0} = {80^o}\)\( \Rightarrow \widehat B > \widehat A=\widehat C\)\( \Rightarrow AC\) là cạnh lớn nhất tam giác ABC (Quan hệ giữa góc và cạnh đối diện trong tam giác)

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