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Bài tập 10 trang 121 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Cho tam giác ABC. Chứng minh rằng giao điểm của hai tia phân giác của hai góc ngoài
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Đề bài

Cho tam giác ABC. Chứng minh rằng giao điểm của hai tia phân giác của hai góc ngoài \(\widehat {{B_1}}\) và \(\widehat {{C_1}}\) (hình 65) nằm trên tia phân giác của góc A.

 

Lời giải chi tiết

 

Gọi D là giao điểm của hai tia phân giác góc \({\widehat B_1}\) và \({\widehat C_1}\).Theo định lí thuận của “Tính chất tia phân giác của một góc” ta có khoảng cách từ D đến AB bằng khoảng cách từ D đến BC và khoảng cách từ D đến AC bằng khoảng cách từ D đến BC.Suy ra khoảng cách từ D đến AB bằng khoảng cách từ M đến AC nên theo định lí đảo của “Tính chất tia phân giác của một góc” ta có D nằm trên tia phân giác của góc A.

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