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Bài 7.2 trang 30 SGK Toán 11 tập 2 – Kết nối tri thức

Cho hình hộp ABCD.A'B'C'D' có các cạnh bằng nhau.

෴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' có các cạnh bằng nhau. Chứng minh rằng tứ diện ACB'D' có các cặp cạnh đối diện vuông góc với nhau.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Nếu đường thẳng a vuông góc với đường thẳng b thì a có vuông góc với các đường thẳng song song với b.

Lời giải chi tiết

+) Vì hình hộp ABCD.A'B'C'D' có các cạnh bằng nhau nên tứ giác A'B'C'D'; ADD'A'; CC'D'D là hình thoi. +) AB' // C'D và C'D \( \bot \) CD' nên AB' \( \bot \)CD' +) AC // A'C' và A'C' \( \bot \) B'D' nên AC \( \bot \) B'D' +) B'C // A'D và A'D \( \bot \) AD' nên B'C \( \bot \) AD' Vậy ta đã chứng minh được rằng tứ diện ACB'D' có các cặp cạnh đối diện vuông góc với nhau.

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

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