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Giải Bài 4 trang 86 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Chứng minh định lí: “Hai đường thẳng phân biệt cùng vuông góc với một đường thẳng thứ ba thì chúng song song với nhau”.

ꦦTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Chứng minh định lí: “Hai đường thẳng phân biệt cùng vuông góc với một đường thẳng thứ ba thì chúng song song với nhau”.

Phương pháp giải - Xem chi tiết

Sử dụng dấu hiệu nhận biết 2 đường thẳng song song.

Lời giải chi tiết

Hình vẽ minh họa:

Viết giả thiết và kết luận bằng kí hiệu:

Chứng minh định lí:Vì a ⊥ c (GT) nên \(\widehat {{A_1}}\)=90°Vì b ⊥ c (GT) nên \(\widehat {{B_1}}\)=90°Do đó \(\widehat {{A_1}}\) = \(\widehat {{B_1}}\) (=90°)Mà \(\widehat {{A_1}}\) và \(\widehat {{B_1}}\) ở vị trí đồng vịSuy ra a // b (Dấu hiệu nhận biết 2 đường thẳng song song).Vậy a // b.

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