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Câu 11 trang 50 SGK Hình học 11 Nâng cao

Cho hình bình hành ABCD nằm trong mặt phẳng (P) và một điểm S nằm ngoài mp(P). Gọi M là điểm nằm giữa S và A ; N là điểm giữa S và B; giao điểm của hai đường thẳng AC và BD là O
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Đề bài

Cho hình bình hành ABCD nằm trong mặt phẳng (P) và một điểm S nằm ngoài mp(P). Gọi M là điểm nằm giữa S và A ; N là điểm giữa S và B; giao điểm của hai đường thẳng AC và BD là O a. Tìm giao điểm của mặt phẳng (CMN) với đường thẳng SO b. Xác định giao tuyến của hai mặt phẳng (SAD) và (CMN)

Lời giải chi tiết

a. Tìm SO ∩ (CNM)Trong mặt phẳng (SAC) gọi I là giao điểm của SO với CMI = SO ∩ CM

\( \Rightarrow \left\{ \begin{array}{l}
I \in SO\\
I \in CM
\end{array} \right.\)

mà CM ⊂ (CMN) nên I = SO ∩ (CMN)b. Tìm (SAD) ∩ (CMN)Trong mp(SBD) gọi K là giao điểm của NI và SDK = NI ∩ SD

\( \Rightarrow \left\{ \begin{array}{l}
K \in NI \subset \left( {CMN} \right)\\
K \in SD \subset \left( {SAD} \right)
✨\end{array} \right. \)\(\Rightarrow K \in \left( {CMN} \right) \cap \left( {SAD} \right)\)

Mà \(M \in \left( {SAD} \right) \cap \left( {CMN} \right)\)Do đó (SAD) ∩ (CMN) = MK

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