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Giải mục 2 trang 29, 30 SGK Toán 11 tập 2 - Kết nối tri thức

Đối với hai cánh cửa trong Hình 7.5, tính góc giữa hai đường mép cửa BC và MN

ওTổng 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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HĐ2

Video hướng dẫn giải

Đối với hai cánh cửa trong Hình 7.5, tính góc giữa hai đường mép cửa BC và MN

Phương pháp giải:

Để xác định góc giữa hai đường thẳng chéo nhau a và b, ta có thể lấy một điểm O thuộc đường thẳng a và qua đó kẻ đường thẳng b' song song với b. Khi đó (a, b) = (a', b')

Lời giải chi tiết:

Vì BC // PN nên (BC, MN) = (PN, MN)

Mà PN vuông góc với MN nên góc giữa hai đường mép này bằng 900.

CH

Video hướng dẫn giải

Nếu đường thẳng a vuông góc với đường thẳng b thì a có vuông góc với các đường thẳng song song với b hay không?

Phương pháp giải:

\(\left. \begin{array}{l}a \bot b\\b//c\end{array} \right\} \Rightarrow a \bot c\)

Lời giải 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.

LT1

Video hướng dẫn giải

Cho tam giác MNP vuông tại N và một điểm A nằm ngoài mặt phẳng (MNP). Lần lượt lấy các điểm B, C, D sao cho M, N, P tương ứng là trung điểm của AB, AC, CD (H.7.7). Chứng minh rằng AD và BC vuông góc với nhau và chéo nhau.

Phương pháp giải:

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:

+) Xét tam giác ABC có M, N lần lượt là trung điểm của AB, AC \( \Rightarrow \) MN là đường trung bình của tam giác ABC \( \Rightarrow \) MN // BC Mà NP \( \bot \) MN nên NP \( \bot \) BC Xét tam giác ADC có N, P lần lượt là trung điểm của AC, CD \( \Rightarrow \) PN là đường trung bình của tam giác ADC \( \Rightarrow \) PN // AD Mà NP \( \bot \) BC nên AD \( \bot \) BC +) BC // MN mà \(MN \subset \left( {MNP} \right) \Rightarrow BC//\left( {MNP} \right)\) PN // AD mà \(PN \subset \left( {MNP} \right) \Rightarrow AD//\left( {MNP} \right)\) Vậy AD và BC chéo nhau.

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