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Giải bài 4.36 trang 68 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình hộp ABCD.A’B’C’D’. Chứng minh rằng:

🐼Tổng 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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Đề bài

Cho hình hộp ABCD.A’B’C’D’. Chứng minh rằng: a) AB’//C’D’;       b) Hai mặt phẳng (AB’D’) và (C’B’D) song song với nhau.

Phương pháp giải - Xem chi tiết

Nếu mặt phẳng \(\left( \alpha  \right)\) chứa hai đường thẳng cắt nhau và hai đường thẳng này song song với mặt phẳng \(\left( \beta  \right)\) thì \(\left( \alpha  \right)\) và \(\left( \beta  \right)\) song song với nhau.

Lời giải chi tiết

a) Tứ giác ABCD và BCC’B’ là hình bình hành nên AD//BC, \(AD = BC\) và BC//B’C’ và \(BC = B'C'\), do đó ADC’B’ là hình bình hành nên AB’//C’D.b) Vì AB’//C’D nên AB’//mp(C’BD)Chứng minh tương tự ta có: AD’//BC’ nên AD’//mp(C’BD). Mặt phẳng (AB’D’) có hai đường thẳng cắt nhau AB’ và AD’ cùng song song với mp(C’BD) nên hai mặt phẳng (AB’D’) và (C’B’D) song song với nhau.

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