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Giải Bài 4 trang 65 sách bài tập toán 7 - CTST

Cho tam giác ABC có AB > AC. Trên tia đối của tia BC lấy điểm M sao cho BM = BA. Trên tia đối của tia CB lấy điểm N sao cho CN = CA.

💃Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Cho tam giác ABC có AB > AC. Trên tia đối của tia BC lấy điểm M sao cho BM  = BA. Trên tia đối của tia CB lấy điểm N sao cho CN = CA. a) Hãy so sánh các góc \(\widehat {AMB}\) và \(\widehat {ANC}\). b) Hãy so sánh các đoạn AM và AN.

Phương pháp giải - Xem chi tiết

Sử dụng mỗi quan hệ giữa góc và cạnh đối diện trong một tam giác để so sánh các góc, các cạnh.

Lời giải chi tiết

a) Ta có AB > AC do đó \(\widehat {ACB} > \widehat {ABC}\) suy ra \(\widehat {ACN} < \widehat {ABM}\)(1)Vì tam giác ANC có CN = CA nên tam giác ANC cân tại C suy ra: \(\widehat {ANC} = \widehat {NAC} = \frac{{{{180}^o} - \widehat {ACN}}}{2}\) (2)Vì tam giác ABM có BM = BA nên tam giác ABM cân tại B suy ra: \(\widehat {AMB} = \widehat {MAB} = \frac{{{{180}^o} - \widehat {ABM}}}{2}\) (3) Từ (1), (2) và (3) suy ra \(\widehat {ANC} > \widehat {AMB}\)b) Trong tam giác ANM, ta có \(\widehat {ANC} > \widehat {AMB}\) suy ra AM > AN

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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