证：在平行四边形ABCD中角AOE=角COF角OAE=角OCFAO=CO（对角线互相平分）所以三角形AOE全等于三角形COFOE=OF
∵AB=CD,∠AOB=∠COD,∠BAO=∠DCO∴△ABO≌△CDO AO=CO又∵∠AOE=∠COF，∠EAO=∠FCO∴△AOE≌△COF ∴OE=OF
