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Giải Bài 27 trang 75 sách bài tập toán 7 - Cánh diều

Cho bốn điểm A, B, C, D nằm trên đường tròn tâm O sao cho AB = CD. Chứng minh \(\widehat {AOB} = \widehat {COD}\)

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

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Đề bài

Cho bốn điểm A, B, C, D nằm trên đường tròn tâm O sao cho AB = CD. Chứng minh \(\widehat {AOB} = \widehat {COD}\)

Phương pháp giải - Xem chi tiết

Xét các điều kiện các cạnh để chứng minh \(\Delta OAB = \Delta 0C{\rm{D}}(c - c - c)\) suy ra \(\widehat {AOB} = \widehat {CO{\rm{D}}}\)

Lời giải chi tiết

 

Vì bốn điểm A, B, C, D nằm trên đường tròn tâm O nên OA = OB = OC = OD.Xét ∆OAB và ∆OCD có:AO = OC (chứng minh trên),AB = DC (giả thiết),OB = OD (chứng minh trên),Suy ra ∆OAB = ∆OCD (c.c.c).Do đó \(\widehat {AOB} = \widehat {CO{\rm{D}}}\) (hai góc tương ứng).Vậy \(\widehat {AOB} = \widehat {CO{\rm{D}}}\)

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