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Giải bài 4 trang 59 vở thực hành Toán 7

Bài 4. Biết rằng tam giác ABC bằng tam giác MNP, \(\widehat {BAC} + \widehat {MNP} = {115^o}\). Hãy tính số đo các góc ACB, MPN.

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

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Đề bài

Bài🍷 4. Biết rằng tam giác ABC bằng tam giác MNP, \(\widehat {BAC} + \widehat {MNP} = {115^o}\). Hãy tính số đo các góc ACB, MPN.

Phương pháp giải - Xem chi tiết

Hai tam giác bằng nhau có các cạnh tương ứng và các góc tương ứng bằng nhau

Lời giải chi tiết

GT \(\Delta ABC = \Delta MNP\),\(\widehat {BAC} + \widehat {MNP} = {115^o}\)
KL Tính \(\widehat {ACB},\widehat {MPN}\)
Vì \(\Delta ABC = \Delta MNP\) nên ta có \(\widehat {ABC} = \widehat {MNP}\)( hai góc tương ứng). Do tổng ba góc trong tam giác ABC bằng \({180^o}\) nên ta có\(\widehat {BAC} + \widehat {ABC} + \widehat {ACB} = {180^o} \Rightarrow \widehat {ACB} = {180^o} - \widehat {BAC} - \widehat {ABC} = {180^o} - {115^o} = {65^o}\)Lại vì \(\Delta ABC = \Delta MNP\) nên \(\widehat {MPN} = \widehat {ACB} = {65^o}\)( hai góc tương ứng).

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