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如圖,連接OE,∵EA⊥EC,ED⊥BE,∴△AEC和△DEB是直角三角形,∵O為平行四邊形的對角線的交點,∴O為AC和BD的中點,∴OE=12AC=12BD,∴AC=BD,∴平行四邊形ABCD為矩形.
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