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Bài 8.8 trang 63 SGK Toán 11 tập 2 - Cùng khám phá

Cho tứ diện ABCD biết ABC và BCD là hai tam giác cân có chung cạnh đáy BC . Gọi I là trung điểm cạnh BC. Chứng minh \(BC \bot (ADI)\).
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Đề bài

Cho tứ diện ABCD biết ABC và BCD là hai tam giác cân có chung cạnh đáy BC . Gọi I là trung điểm cạnh BC. Chứng minh \(BC \bot (ADI)\).

Phương pháp giải - Xem chi tiết

Dựa vào tam giác cân để suy ra \(AI \bot BC\) và \(DI \bot BC\)

Lời giải chi tiết

Vì \(\Delta ABC\) cân tại \(A\) và \(I\) là trung điểm của \(BC\) nên \(AI \bot BC\)Vì \(\Delta DBC\) cân tại \(D\) và \(I\) là trung điểm của \(BC\) nên \(DI \bot BC\)Ta có \(\left\{ \begin{array}{l}BC \bot AI\\BC \bot DI\end{array} \right. \Rightarrow BC \bot \left( {AID} \right)\)

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