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Bài 7.18 trang 53 SGK Toán 11 tập 2 - Kết nối tri thức

Cho hình hộp chữ nhật ABCD. A'B'C'D'.

𓆉Tổng 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 chữ nhật ABCD.A'B'C'D'. a) Chứng minh rằng (BDD′B′) \( \bot \) (ABCD). b) Xác định hình chiếu của AC′ trên mặt phẳng (ABCD). c) Cho AB = a, BC = b, CC′ = c. Tính AC′.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Hai mặt phẳng được gọi là vuông góc nếu một đường thẳng nằm trong mặt phẳng này vuông góc với mặt phẳng kia.

Lời giải chi tiết

 

a) Ta có \(BB' \bot \left( {ABCD} \right);BB' \subset \left( {BDD'B'} \right) \Rightarrow \left( {BDD'B'} \right) \bot \left( {ABCD} \right)\). b) A là hình chiếu của A trên (ABCD). C là hình chiếu của C’ trên (ABCD) do \(CC' \bot \left( {ABCD} \right)\). \( \Rightarrow \) AC là hình chiếu của AC’ trên (ABCD). c) Xét tam giác ABC vuông tại B có: \(A{C^2} = A{B^2} + B{C^2} = {a^2} + {b^2} \). Xét tam giác AC’C vuông tại C có: \(A{C'^2} = C{C'^2} + A{C^2} = {c^2} + {a^2} + {b^2} \Rightarrow A'C = \sqrt {{a^2} + {b^2} + {c^2}} \).

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