answer: the missing part is cpct.
explanation:
here, we have, a quadrilateral abcd.
in which, diagonals ac and bd are bisecting each other. and, o is the point of intersection of line segments ac and bd. and, angle aob is labeled as 1, angle boc is labeled as 4, angle cod is labeled as 2 and angle aod is labeled as 3.
proof : abcd is a parallelogram.
now, for triangles aob and cod,
angle 1 = angle 2 (because, they are vertical angles)
ao=oc and bo=od (because , it is given that diagonals bisect each other. )
(by sas postulate)
similarly, triangles aod and cob are congruent.
by cpct("corresponding parts of congruent triangles are congruent"),
and,
as the alternate interior angles are congruent the opposite sides of quadrilateral abcd are parallel,
therefore, abcd is a parallelogram.