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Giải bài 3.29 trang 80 SGK Toán 8 - Cùng khám phá

Cho hình chữ nhật
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Đề bài

Cho hình chữ nhật \(ABCD\) và \(M,N,P,Q\) lần lượt là trung điểm các cạnh \(AB,BC,CD,AD\). Chứng minh rằng \(MNPQ\) là hình thoi.

Phương pháp giải - Xem chi tiết

Dựa vào tính chất hình chữ nhật và hình thoi để chứng minh

Lời giải chi tiết

Xét tam giác \(MBN\) và \(NCP\), ta có:\(BN = NC\) (N là trung điểm)\(\widehat {MBN} = \widehat {NCP} = 90^\circ \) (do \(ABCD\) là hình chữ nhật)\(MB = CP\) (do \(M\) và \(P\) lần lượt là trung điểm của \(AB\) và \(CD\))→   \(\Delta MBN = \Delta NCP\)→   \(\Delta MBN = \Delta AMQ = \Delta NCP = \Delta QDP\)→   \(MQ = MN = NP = QP\) (các cạnh tương ứng)→   Tứ giác \(MNPQ\) là hình thoi

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