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Giải Bài 10 trang 84 SGK Toán 7 tập 2 - Chân trời sáng tạo

Trên đường thẳng a lấy ba điểm phân biệt I, J, K (J ở giữa I và K). Kẻ đường thẳng b vuông góc với a tại J, trên b lấy điểm M khác điểm J. Đường thẳng qua I vuông góc với MK cắt b tại N. Chứng minh rằng KN vuông góc với MI.

🐟Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

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Đề bài

Trên đường thẳng a lấy ba điểm phân biệt I, J, K (J ở giữa I và K). Kẻ đường thẳng b vuông góc với a tại J, trên b lấy điểm M khác điểm J. Đường thẳng qua I vuông góc với MK cắt b tại N. Chứng minh rằng KN vuông góc với MI.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Ta chứng minh N là trực tâm của tam giác MIK

Lời giải chi tiết

Vì b vuông góc với a tại J (theo giả thiết) và M thuộc b\( \Rightarrow MJ \bot IK\)(1)Vì đường thẳng qua I vuông góc với MK và cắt b tại N (gọi C là giao của MK và đường thẳng qua I vuông góc với MK)\( \Rightarrow MK \bot IC\)(2)Từ (1) và (2)\( \Rightarrow \)N là trực tâm ΔMIK\( \Rightarrow \)NK là đường cao của ΔMIK (Các đường cao trong tam giác đi qua trực tâm)\( \Rightarrow \)KN \( \bot \)MI 

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