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Giải bài 8 trang 65 sách bài tập toán 8 - Chân trời sáng tạo

Cho hình bình hành ABCD có hai đường chéo cắt nhau tại O. Gọi M và N lần lượt là trung điểm của OB và OD. Chứng minh tứ giác AMCN là hình bình hành.

💯Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

Cho hình bình hành ABCD có hai đường chéo cắt nhau tại O. Gọi M và N lần lượt là trung điểm của OB và OD. Chứng minh tứ giác AMCN là hình bình hành.

Phương pháp giải - Xem chi tiết

+ Sử dụng kiến thức về tính chất hình bình hành để chứng minh: Hình bình hành có hai đường chéo cắt nhau tại trung điểm của mỗi đường. + Sử dụng kiến thức về dấu hiệu nhận biết hình bình hành để chứng minh: Tứ giác có hai đường chéo cắt nhau tại trung điểm của mỗi đường là hình bình hành.

Lời giải chi tiết

Tứ giác ABCD là hình bình hành nên \(OA = OC\), \(OB = OD\)Mà: \(ON = \frac{1}{2}OD\) (do N là trung điểm của OD)\(OM = \frac{1}{2}OB\) (do M là trung điểm của OB)Do đó, \(OM = ON\)Tứ giác AMCN có: \(OM = ON\) (cmt), \(OA = OC\) (cmt) nên tứ giác AMCN là hình bình hành.

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