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Giải Bài 4 trang 68 sách bài tập toán 7 - Cánh diều

Bạn Bình phát biểu: “Không có tam giác ABC nào mà

𝔍Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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Đề bài

Bạn Bình phát biểu: “Không có tam giác ABC nào mà ဣ\(\widehat {A} = 3\widehat {B},\widehat B = 3\widehat C\) và \(\widehat C = {14^o}\) ”. Phát biểu của bạn Bình có đúng không? Vì sao?

Phương pháp giải - Xem chi tiết

Tính số đo các góc A, B, C dựa vào phát biểu của bạn Bình từ đó đưa ra kết luận bạn Bình phát biểu đúng không?

Lời giải chi tiết

Giả sử có tam giác ABC thỏa mãn \(\widehat {{A^{}}} = 3\widehat B\) và \(\widehat B = 3\widehat C\)Khi đó \(\widehat {{A^{}}} = 3\widehat B = 3.3\widehat C = 9\widehat C\) và \(\widehat B = 3\widehat C\)Suy ra \(\widehat {{A^{}}} + \widehat B + \widehat C = 9\widehat C + 3\widehat C + \widehat C = 13\widehat C\)Mà \(\widehat C = {14^o}\)Do đó \(\widehat {{A^{}}} + \widehat B + \widehat C = {13.14^o} = {182^o}\) . Điều này vô lí (vì tổng các góc của tam giác bằng 180°).Do đó không có tam giác ABC nào thỏa mãn điều kiện \(\widehat {A} = 3\widehat {B},\widehat B = 3\widehat C\) và \(\widehat C = {14^o}\)Vậy bạn Bình phát biểu đúng.

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