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Thử tài bạn trang 109 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Dựa vào hình 36, hãy viết giả thiết, kết luận và chứng minh định lí theo gợi ý sau:
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Đề bài

Dựa vào hình 36, hãy viết giả thiết, kết luận và chứng minh định lí theo gợi ý sau: Gọi I là giao điểm của hai đường phân giác xuất phát từ đỉnh B và C của tam giác ABC, kẻ \(IM \bot BC,\,\,IE \bot AB,\,\,IN \bot AC\) (xem hình vẽ). Hãy chứng minh: * IM = IN = IE * AI là tia phân giác của góc A.

 

Lời giải chi tiết

 Chứng minh:a) Ta có I nằm trên tia phân giác của \(\eqalign{  & \widehat {ABC}(gt),IE \bot AB(gt),IM \bot BC(gt)  \cr  &  \Rightarrow IE = IM(1) \cr}\)Ta cũng có I nằm trên tia phân giác của \(\eqalign{  & \widehat {ACB},IM \bot BC(gt),IN \bot AC(gt)  \cr  &  \Rightarrow IM = IN \cr}\)Từ (1) và (2) ta có IM = IN = IE.b) Ta có \(IE \bot AB,IN \bot AC\) và IE = IN => I nằm trên tia phân giác của \(\widehat {BAC}\)Vậy AI là tia phân giác của \(\widehat {BAC}.\)

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