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Bài tập 23 trang 123 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Hình 73 minh họa cho cách dựng đường thẳng đi qua một điểm và vuông góc với đường thẳng cho trước bằng thước kẻ và compa.
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Đề bài

Hình 73 minh họa cho cách dựng đường thẳng đi qua một điểm và vuông góc với đường thẳng cho trước bằng thước kẻ và compa. Cho đường thẳng d và điểm M không nằm trên đường thẳng d.

 

- Lấy M làm tâm, vẽ một cung trong cắt đường thẳng d tại hai điểm A và B \(\left( {A \ne B} \right)\)  (1) - Lấy A, B làm tâm vẽ hai cung trong (cùng bán kính trên) cắt nhau tại C \(\left( {C \ne M} \right)\)  (2) - Vẽ đường thẳng MC (3) Hãy chứng minh MC vuông góc với d.

Lời giải chi tiết

Ta có CA = CB (cùng bằng bán kính của đường tròn tâm M)=> C thuộc đường trung trực của đoạn thẳng AB (1)Mà MA = MB (MA, MB là bán kính của đường tròn tâm M)=> M thuộc đường trung trực của đoạn thẳng AB (2)Từ (1) và (2) ta có MC là đường trung trực của đoạn thẳng AB => \(MC \bot d.\)

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