QUICK! 30 POINTS! Clara's proof

For triangles AOB and COD, angle 1 is equal to angle 2, as they are vertical angles.
AO = OC and BO = OD because it is given that diagonals bisect each other.
The triangles AOB and COD are congruent by SAS postulate.
Similarly, triangles AOD and COB are congruent.
By , angle ABD is equal to angle CDB and angle ADB is equal to angle CBD.
As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel.
Therefore, ABCD is a parallelogram.

Which is the missing phrase in Clara's proof?
CPCTC
property of parallelograms
transitive property
vertical angles theorem