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Giải bài 2 trang 78 vở thực hành Toán 8

Cho tứ giác ABCD, gọi E, F, K lần lượt là trung điểm của AD, BC, AC.

🐼Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

Cho tứ giác ABCD, gọi E, F, K lần lượt là trung điểm của AD, BC, AC. a) Chứng minh EK // CD, FK // AB.

🌱b) So sánh EF và \(\frac{1}{2}\left( {AB + CD} \right).\)

Phương pháp giải - Xem chi tiết

Dựa vào tính chất đường trung bình của tam giác.

Lời giải chi tiết

a) ∆ABC có F là trung điểm BC, K là trung điểm AC nên FK là đường trung bình của ∆ABC, suy ra FK // AB.∆ACD có E là trung điểm AD nên EK là đường trung bình của ∆ACD, suy ra EK // CD.b) FK là đường trung bình của ∆ABC nên AB = 2FK.Tương tự CD = 2EK.

𝄹Ta có FK + KE ≥ FE nên \(\frac{1}{2}\left( {AB + CD} \right) \ge EF.\)

꧟Do đó \(EF\le \;\frac{1}{2}\left( {AB + CD} \right).\)

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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