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Giải bài 39 trang 113 sách bài tập toán 11 - Cánh diều

Cho hình lăng trụ tam giác \(ABC.A'B'C'\). Gọi \(M\), \(N\) lần lượt là trung điểm của \(A'B'\), \(B'C'\).

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

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Đề bài

Cho hình lăng trụ tam giác \(ABC.A'B'C'\). Gọi \(M\), \(N\) lần lượt là trung điểm của \(A'B'\), \(B'C'\). Gọi \(d\) là giao tuyến của hai mặt phẳng \(\left( {BMN} \right)\) và \(\left( {ACC'A'} \right)\). Khẳng định nào sau đây là đúng? A. \(d\parallel AA'\)                         B. \(d\parallel BC\)                 C. \(d\parallel B'C'\)               D. \(d\parallel A'C'\)

Phương pháp giải - Xem chi tiết

Sử dụng các tính chất về giao tuyến của hai mặt phẳng có chứa hai đường thẳng song song.

Lời giải chi tiết

Do \(M\) là trung điểm của \(A'B'\), \(N\) là trung điểm của \(B'C'\) nên \(MN\) là đường trung bình của tam giác \(A'B'C'\). Suy ra \(MN\parallel A'C'\).Vì \(MN \subset \left( {BMN} \right)\), \(A'C' \subset \left( {ACC'A'} \right)\) và \(d = \left( {BMN} \right) \cap \left( {ACC'A'} \right)\) nên suy ra \(d\parallel A'C'\).Đáp án đúng là D.

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