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Giải bài 3 trang 80 SGK Toán 8 tập 1– Chân trời sáng tạo

Cho 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 \(ABCD\). Gọi \(E\) là trung điểm của \(AD\), \(F\) là trung điểm của \(BC\)

📖a) Chứng minh rằng tứ giác \(EBFD\) là hình bình hành

💃b) Gọi \(O\) là giao điểm của hai đường chéo của hình bình hành \(ABCD\). Chứng minh rằng ba điểm \(E\), \(O\), \(F\) thẳng hàng.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng dấu hiệu nhận biết của hình bình hành

Lời giải chi tiết

a) Vì \(ABCD\) là hình bình hành (gt)

Suy ra \(AD = BC\); \(AD\) // \(BC\)

൲Mà \(E\), \(F\) là trung điểm của \(AD\), \(BC\) (gt)

Suy ra \(AE = ED = BF = FC\)

Xét tứ giác \(EBFD\) ta có:

\(ED = FB\) (cmt)

\(ED\) // \(BF\) (do \(AD\) // \(BC\))

Suy ra \(EDFB\) là hình bình hành

b) Vì \(ABCD\) là hình bình hành (gt)

Suy ra \(O\) là trung điểm của \(AC\) và \(BD\)

Mà \(DEBF\) là hình bình hành (gt)

Suy ra \(O\) cũng là trung điểm của \(EF\)

Suy ra \(E\), \(O\), \(F\) thẳng hàng

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