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Giải Bài 86 trang 94 sách bài tập toán 7 - Cánh diều

Cho tam giác ABC cân ở A. Đường trung trực của cạnh AC cắt AB tại D. Biết CD là tia phân giác của góc ACB. Tính số đo các góc của tam giác ABC.

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

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Đề bài

Cho tam giác ABC cân ở A. Đường trung trực của cạnh AC cắt AB tại D. Biết CD là tia phân giác của góc ACB. Tính số đo các góc của tam giác ABC.

Phương pháp giải - Xem chi tiết

- Sử dụng tính chất ba đường trung trực và tía phân giác trong tam giác cân, tổng ba góc của một tam giác để tính các số đo góc của tam giác ABC.

Lời giải chi tiết

 

Đặt \(\widehat {DCA} = x\).Vì CD là tia phân giác của góc ACB nên \(\widehat {ACB} = 2\widehat {ACD} = 2\widehat {BCD} = 2x\)Vì tam giác ABC cân tại A nên AB = AC, \(\widehat {ABC} = \widehat {ACB}\)Suy ra \(\widehat {ABC} = 2x\)Do điểm D nằm trên đường trung trực của canhk AC nên DA = DC.Do đó tam giác DAC cân ở D nên \(\widehat {DAC} = \widehat {DCA} = x\).Xét ∆ABC có \(\widehat {ACB} + \widehat {ABC} + \widehat {BAC} = 180^\circ \) (tổng ba góc của một tam giác)Hay 2x + 2x + x = 180° nên 5x = 180°.Suy ra x = 180°: 5 = 36°.Do đó \(\widehat {ACB} = \widehat {ABC} = 2.36^\circ  = 72^\circ ,\widehat {BAC} = 36^\circ \)

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