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Giải mục 1 trang 44, 45 SGK Toán 11 tập 2 - Kết nối tri thức

Cho hai mặt phẳng (P) và (Q). Lấy hai đường thẳng a, a' cùng vuông góc với (P)

꧒Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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HĐ1

Video hướng dẫn giải

ཧCho hai mặt phẳng (P) và (Q). Lấy hai đường thẳng a, a' cùng vuông góc với (P), hai đường thẳng b, b' cùng vuông góc với (Q). Tìm mối quan hệ giữa các góc (a,b) và (a', b').

Phương pháp giải:

- Hai đường thẳng phân biệt cùng vuông góc với một mặt phẳng thì song song với nhau. - Nếu b // b’ thì (a, b) = (a, b’).

Lời giải chi tiết:

Vì hai đường thẳng a, a' cùng vuông góc với (P), hai đường thẳng b, b' cùng vuông góc với (Q) nên a // a',  b // b' Vậy (a,b) = (a', b')

CH1

Video hướng dẫn giải

Góc giữa hai mặt phẳng bằng 00 khi nào, khác 00 khi nào?

Phương pháp giải:

Vị trí tương đối 2 mặt phẳng

Lời giải chi tiết:

Góc giữa hai mặt phẳng

+) bằng 00 khi trùng nhau

+) khác 00 khi giao nhau

LT1

Video hướng dẫn giải

Cho hình chóp S.ABCD, đáy ABCD là một hình chữ nhật có tâm O, SO \( \bot \) (ABCD). Chứng minh rằng hai mặt phẳng (SAC) và (SBD) vuông góc với nhau khi và chỉ khi ABCD là một hình vuông.

Phương pháp giải:

Sử dụng nhận xét trang 45 để xác định góc giữa 2 mặt phẳng.

Lời giải chi tiết:

 

\(\left. \begin{array}{l}\left( {SAC} \right) \cap \left( {SBD} \right) = SO\\\left( {SAC} \right):AC \bot SO = \left\{ O \right\}\\\left( {SBD} \right):BD \bot SO = \left\{ O \right\}\end{array} \right\} \Rightarrow \left( {\left( {SAC} \right),\left( {SBD} \right)} \right) = \left( {AC,BD} \right) = \widehat {AOB}\) +) Nếu \(\left( {SAC} \right) \bot \left( {SBD} \right) \Rightarrow \widehat {AOB} = {90^0} \Rightarrow AC \bot BD\) Mà ABCD là hình chữ nhật nên ABCD là hình vuông. +) Nếu ABCD là hình vuông \( \Rightarrow AC \bot BD \Rightarrow \widehat {AOB} = {90^0}\) \( \Rightarrow \left( {\left( {SAC} \right),\left( {SBD} \right)} \right) = {90^0} \Rightarrow \left( {SAC} \right) \bot \left( {SBD} \right)\)

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

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