The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:
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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 ______________ are congruent by the Alternate Interior Angles Theorem. Angles ______________ are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the Alternate Interior Theorem. 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 angles accurately complete the proof?