100 points!!!!!
The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:
According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.
What theorems accurately complete the proof?