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Giải bài 8 trang 75 vở thực hành Toán 7

Bài 8. Cho điểm A nằm trên trung trực của đoạn thẳng BC sao cho \(\widehat {ABC} = {60^o}\). Chứng minh rằng CA = CB.

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

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Đề bài

Bài𝔍 8. Cho điểm A nằm trên trung trực của đoạn thẳng BC sao cho \(\widehat {ABC} = {60^o}\). Chứng minh rằng CA = CB.

Phương pháp giải - Xem chi tiết

Chứng minh ABC là tam giác đều

Lời giải chi tiết

GT d là trung trực BC, \(A \in BC,\widehat {ABC} = {60^o}\)
KL  CA = CB.
Do A thuộc trung trực BC nên AB = AC hay  \(\Delta ABC\)cân tại A.Từ đây suy ra \(\widehat {ACB} = \widehat {ABC} = {60^o}\). Do tổng ba góc trong tam giác ABC bằng \({180^o}\)nên:\(\widehat {BAC} = {180^o} - \widehat {ACB} - \widehat {ABC} = {60^o}\)Vậy tam giác ABC có ba góc bằng nhau nên ABC là tam giác đều và do đó CA = CB.

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