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Giải bài 5 trang 108 SGK Toán 8 tập 1 - Cánh diều

Bạn Hoa vẽ tam giác ABC lên tờ giấy sau đó cắt một phần tam giác ở phái góc (Hình 44). Bạn Hoa đó bạn Hùng: Không vẽ lại tam giác ABC, làm thế nào tính được độ dài đoạn thẳng AC, BC và số đo góc ACB? Bạn Hùng làm như sau: - Qua điểm A kẻ đường thẳng d song song với BC; qua điểm B kẻ đường thẳng d’ song song với AC. - Gọi E là giao điểm của d và d’. - Đo độ dài các đoạn thẳng AE, BE và đo góc AEB. Từ đó, tính được độ dài các đoạn thẳng AC, BC và số đo góc ACB (hình 45). Em hãy giải thích

ಞTổng 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

Bạn Hoa vẽ tam giác ABC lên tờ giấy sau đó cắt một phần tam giác ở phái góc (Hình 44). Bạn Hoa đó bạn Hùng: Không vẽ lại tam giác ABC, làm thế nào tính được độ dài đoạn thẳng AC, BC và số đo góc ACB?

Bạn Hùng làm như sau: - Qua điểm A kẻ đường thẳng d song song với BC; qua điểm B kẻ đường thẳng d’ song song với AC. - Gọi E là giao điểm của d và d’. - Đo độ dài các đoạn thẳng AE, BE và đo góc AEB. Từ đó, tính được độ dài các đoạn thẳng AC, BC và số đo góc ACB (hình 45). Em hãy giải thích cách làm của bạn Hùng.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh ACBE là hình bình hành.

Lời giải chi tiết

Qua A kẻ đường thẳng d//BC, qua B kẻ đường thẳng \(d'//AC\)Mà E là giao điểm của d và \(d'\)Suy ra AC//BE; AE//BC.Tứ giác ACBE là hình bình hành.Suy ra AC = BE; BC = AE; \(\widehat {ACB} = \widehat {AEB}\)

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