AO=CO ....AC and BD bisect each other
BO=DO ....AC and BD bisect each other
∠ABO=∠COD ...Vertically opposite angles
△AOB≅△COD ...[SAS test]
⇒∠BAO i.e., ∠BAC=∠ABO i.e., ∠ABD
⇒AC∥BD
Again, △AOD≅△COB ...[SAS test]
⇒AD∥CB
⇒ABCD is a cyclic parallelogram.
⇒∠DAC=∠DBA.............. (1)
[Opp.angles of a parallelogram are equal]
Also, ACBD is a cyclic quadrilateral
Therefore ∠DAC+∠DBA=180∘................ (2)
From (1) and (2), we get
∠DAC=∠DBA=90∘
Hence, ABCD is a rectangle.