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Giải bài 5 trang 57 SGK Toán 8 – Cánh diều

Cho đoạn thẳng AB. Hãy trình bày cách chia đoạn thẳng AB thành ba đoạn thẳng bằng nhau mà không cần dùng thước đo.

🍰Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Cho đoạn thẳng AB. Hãy trình bày cách chia đoạn thẳng AB thành ba đoạn thẳng bằng nhau mà không cần dùng thước đo.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Lấy thêm điểm và sử dụng định lý Thales để chia đoạn thẳng thành ba phần bằng nhau.

Lời giải chi tiết

Lấy một điểm P nằm ngoài đoạn thẳng AB và nối AP, BP. Trên đoạn thẳng AP lấy hai điểm M và N sao cho AM = MN = NP. Khi đó \(\frac{{AM}}{{AP}} = \frac{1}{3};\,\,\frac{{AN}}{{AP}} = \frac{2}{3}\). Kẻ các đoạn thẳng \(MC\parallel PB,\,\,ND\parallel PB\) với \(C,\,\,D \in AB\). Theo hệ quả của định lý Thales trong tam giác APB thì \(\frac{{AM}}{{AP}} = \frac{{AC}}{{AB}} = \frac{1}{3}\) và \(\frac{{AN}}{{AP}} = \frac{{AD}}{{AB}} = \frac{2}{3}\). Khi đó AC = CD = DB = \(\frac{1}{3}\)AB. Vậy ta đã chia đoạn thẳng AB thành 3 phần bằng nhau mà không cần dùng thước đo.

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