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Bài 7.3 trang 30 SGK Toán 11 tập 2 – Kết nối tri thức

Cho tứ diện ABCD có (widehat {CBD} = {90^0}.)

ღTổng 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 tứ diện ABCD có \(\widehat {CBD} = {90^0}.\) a) Gọi M, N tương ứng là trung điểm của AB, AD. Chứng minh rằng MN vuông góc BC. b) Gọi G, K tương ứng là trọng tâm của các tam giác ABC, ACD. Chứng minh rằng GK vuông góc với BC.

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

a) Xét tam giác ABD có M, N tương ứng là trung điểm của AB, AD \( \Rightarrow \) MN là đường trung bình của tam giác ABD  \( \Rightarrow \)  MN // BD mà BD \( \bot \) BC (\(\widehat {CBD} = {90^0}\)) \( \Rightarrow \) MN \( \bot \) BC. b) Vì G, K tương ứng là trọng tâm của các tam giác ABC, ACD nên \(\frac{{CG}}{{CM}} = \frac{{CK}}{{CN}} = \frac{2}{3}\) \( \Rightarrow \) GK // MN (Định lý Talet) mà MN \( \bot \) BC \( \Rightarrow \) GK \( \bot \) BC.

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

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