(1)要证OA=OB,由等角对等边需证∠CAB=∠DBA,由已知△ABC≌△BAD即可证.
(2)要证AB∥CD,根据平行线的性质需证∠CAB=∠ACD,由已知和(1)可证∠OCD=∠ODC,又因为
∠AOB=∠COD,所以可证∠CAB=∠ACD,即AB∥CD获证.
证明:(1)∵△ABC≌△BAD,
∴∠CAB=∠DBA,
∴OA=OB.
(2)∵△ABC≌△BAD,
∴AC=BD,
又∵OA=OB,
∴AC-OA=BD-OB,
即:OC=OD,
∴∠OCD=∠ODC,
∵∠AOB=∠COD,∠CAB=,∠ACD=,
∴∠CAB=∠ACD,
∴AB∥CD.