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Giải bài 4.37 trang 87 SGK Toán 7 tập 1 - Kết nối tri thức

Cho M, N là hai điểm phân biệt nằm trên đường trung trực của đoạn thẳng AB sao cho AM = AN. Chứng minh rằng MB = NB và góc AMB bằng góc ANB.

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

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

Cho M, N là hai điểm phân biệt nằm trên đường trung trực của đoạn thẳng AB sao cho AM = AN. Chứng minh rằng MB = NB và góc AMB bằng góc ANB.

Phương pháp giải - Xem chi tiết

Hình thoi là tứ giác có 4 cạnh của tứ giác bằng nhau.

Lời giải chi tiết

Vì M, N nằm trên đường trung trực của AB nên MA = MB ; NA = NB ( tính chất)Mà MA = NA (gt)Do đó, MA = NA = MB = NB.Xét tam giác AMB và tam giác ANB có:MA = NA (gt)MB = NB (cmt)AB chungDo đó, ∆AMB = ∆ANB (c – c – c).\(\Rightarrow \widehat{AMB}=\widehat{ANB}\) (2 góc tương ứng).Vậy MB = NB và góc AMB bằng góc ANB.

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