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Giải bài 30 trang 108 sách bài tập toán 11 - Cánh diều

Cho hình chóp \(S.ABCD\) có đáy\(ABCD\) là hình bình hành.

ಞTổng 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

 hình chóp \(S.ABCD\) có đáy\(ABCD\) là hình bình hành. Gọi \(M\), \(N\), \(P\) lần lượt là trung điểm của \(AB\), \(CD\), \(SA\). Khẳng định nào sau đây là đúng? A. \(\left( {SBN} \right)\parallel \left( {DAP} \right)\)                               B. \(\left( {SBC} \right)\parallel \left( {MPD} \right)\) C. \(\left( {SBN} \right)\parallel \left( {PMD} \right)\)                              D. \(\left( {SDN} \right)\parallel \left( {MAP} \right)\)

Phương pháp giải - Xem chi tiết

Sử dụng các tính chất về hai mặt phẳng song song.

Lời giải chi tiết

Xét mặt phẳng \(\left( {ABCD} \right)\), ta thấy rằng \(BN\) cắt \(AD\).Mà \(BN \subset \left( {SBN} \right)\), \(AD \subset \left( {DAP} \right)\), ta suy ra \(\left( {SBN} \right)\) và \(\left( {DAP} \right)\) có điểm chung, tức hai mặt phẳng này không song song với nhau.Tương tự, do \(MD\) cắt \(BC\) nên \(\left( {SBC} \right)\) và \(\left( {MPD} \right)\) không song song với nhau.Do \(M\) là trung điểm \(AB\), \(P\) là trung điểm của \(SA\), ta suy ra \(MP\) là đường trung bình của tam giác \(SAB\). Suy ra \(MP\parallel SB\). Do \(MP \subset \left( {DMP} \right)\), ta kết luận rằng \(SB\parallel \left( {DMP} \right)\). Chứng minh tương tự ta cũng có \(BN\parallel \left( {DMP} \right)\). Như vậy \(\left( {SBN} \right)\parallel \left( {PMD} \right)\).Vì \(S \in \left( {SDN} \right) \cap \left( {MAP} \right)\), nên hai mặt phẳng này không song song với nhau.Đáp án đúng là C.

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