1、∵ AB ∥ DC,AD ∥ BC,
∴ ∠BAC = ∠DCA,∠BCA = ∠DAC.
在△ABC和△CDA中,
∵∠BAC = ∠DCA,AC = CA,
∠BCA = ∠DAC,
∴ △ABC ≌ △CDA(ASA). ∴ AB = DC,
AD = BC.
2、在△ABE和△ACD中,
∵∠A = ∠A,AB = AC,∠B = ∠C,
∴ △ABE ≌ △ACD(ASA).
∴ AD = AE.
∴ AB - AD = AC - AE.即DB = EC.
3、∵ ∠3 + ∠AOB = ∠4 + ∠AOC = 180°,∠3 = ∠4,
∴∠AOB = ∠AOC.在△AOB和△AOC中,
∵ ∠1 = ∠2, AO = AO,∠AOB = ∠AOC,
∴ △AOB ≌ △AOC(ASA).
∴ OB = OC.