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證明:∵EF是BD的垂直平分線,∴EB=ED,∴∠EBD=∠EDB.∵BD是△ABC的角平分線,∴∠EBD=∠FBD.∴∠FBD=∠EDB,∴ED‖BF.同理,DF‖BE,∴四邊形BFDE是平行四邊形.又∵EB=ED,∴四邊形BFDE是菱形.
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