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Bài 2 trang 79 SGK Toán 11 tập 2 - Cánh Diều

Trong Hình 7 cho ABB’A’, BCC’B’, ACC’A’ là các hình chữ nhật. Chứng minh rằng (AB bot CC',,,,AA' bot BC)

🐽Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Trong Hình 7 ꩲcho ABB’A’, BCC’B’, ACC’A’ là các hình chữ nhật. Chứng minh rằng \(AB \bot CC',\,\,\,AA' \bot BC\)

Phương pháp giải - Xem chi tiết

꧒Dựa vào kiến thức hai đường thẳng vuông góc để xác định

Lời giải chi tiết

-         Chứng minh \(AB \bot CC'\)

+ ♉Do ABB’A’ là hình chữ nhật \( \Rightarrow AB \bot BB'\) (1)

+ 💞Do BCC’B’ là hình chữ nhật \( \Rightarrow BB' //CC'\) (2)

Từ (1) và (2) \( \Rightarrow AB \bot CC'\) (đpcm)Chứng minh tương tự:

+ 🍃Do BCC’B’ là hình chữ nhật \( \Rightarrow BC \bot CC'\)

+ ꦅDo AA'C'C là hình chữ nhật \( \Rightarrow AA' //CC'\) 

Từ đó \( \Rightarrow AA' \bot BC\) (đpcm)

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