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Giải bài 5 trang 58 SGK Toán 7 tập 2 - Chân trời sáng tạo

Cho đoạn thẳng AB có O là trung điểm. Vẽ hai đường thẳng m và n lần lượt vuông góc với AB tại A và B. Lấy điểm C trên m, CO cắt n tại D (Hình 24). Chứng minh rằng O là trung điểm CD.

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Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Cho đoạn thẳng AB có O là trung điểm. Vẽ hai đường thẳng m và n lần lượt vuông góc với AB tại A và B. Lấy điểm C trên m, CO cắt n tại D (Hình 24). Chứng minh rằng O là trung điểm CD.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Chứng minh tam giác OAC và tam giác OBD bằng nhau - Từ đó suy ra OC = OD ( 2 cạnh tương ứng)

Lời giải chi tiết

Xét \(\Delta OAC\) và \(\Delta OBD\), ta có:\(\widehat {COA} = \widehat {BOD}\) ( 2 góc đối đỉnh)AO = BO\(\widehat A = \widehat B\)\(\Rightarrow \Delta OAC=\Delta OBD\) ( g-c-g )\( \Rightarrow CO = DO\) ( cạnh tương ứng )\( \Rightarrow \) O là trung điểm CD

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