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Giải bài 7.8 trang 28 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho tứ diện \(ABCD\) có \(AB = AC\) và \(DB = DC\). Chứng minh rằng \(AD \bot BC\).

𒀰Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

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

Cho tứ diện \(ABCD\) có \(AB = AC\) và \(DB = DC\). Chứng minh rằng \(AD \bot BC\).

Phương pháp giải - Xem chi tiết

Gọi \(M\) là trung điểm của \(BC\) chứng minh \(BC \bot \left( {AMD} \right)\), suy ra \(BC \bot AD\).

Lời giải chi tiết

Gọi \(M\) là trung điểm của \(BC\), ta có: \(BC \bot AM,BC \bot MD\).Do đó \(BC \bot \left( {AMD} \right)\), suy ra \(BC \bot AD\).

 

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