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Bài 4.2 trang 94 SGK Toán 11 tập 1 - Cùng khám phá

Trong mặt phẳng (P), cho hình bình hành ABCD. Lấy S nằm ngoài mặt phẳng (P). Lấy M, N lần lượt là các điểm nằm trên các cạnh SA, SC.
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Đề bài

Trong mặt phẳng (P), cho hình bình hành ABCD. Lấy S nằm ngoài mặt phẳng (P). Lấy M, N lần lượt là các điểm nằm trên các cạnh SA, SC. a) Chứng minh rằng đường thẳng MN nằm trong mặt phẳng (SAC). b) Giả sử MN và AC cắt nhau tại I, chứng minh I là điểm chung của hai mặt phẳng (BMN) và (ABC), từ đó suy ra giao tuyển của hai mặt phẳng (BMN) và (ABC).

Phương pháp giải - Xem chi tiết

a) Đường thẳng có 2 điểm phân biệt nằm trong mặt phẳng thì đường thẳng đó cũng thuộc vào mặt phẳng. b) Nếu 2 điểm A, B cùng thuộc 2 mặt phẳng phân biệt (P) và (Q) thì AB là giao tuyến của (P) và (Q).

Lời giải chi tiết

a)\(\left\{ \begin{array}{l}M \in SA\\N \in SC\end{array} \right. \Rightarrow MN \subset \left( {SAC} \right)\)b)\(\begin{array}{l}I = MN \cap AC\\\left\{ \begin{array}{l}MN \subset \left( {BMN} \right)\\AC \subset \left( {ABC} \right)\end{array} \right.\end{array}\)Nên I là điểm chung của (BMN) và (ABC)\( \Rightarrow BI = \left( {BMN} \right) \cap \left( {ABC} \right)\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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