The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: According to the given information, and . 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?

Given a parallelogram ABCD, refer to the attached image.To prove: Opposite angles are congruent.Proof:According to the given information,Step 1: Using a straightedge, extend segment AB and place point P above point B. Step 2: By the same reasoning, extend segment AD and place point T to the left of point A.Step 3: Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem.Step 4: Angles PBC and BAD are congruent by the Corresponding Angles Theorem. ( If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.)Step 5: By the Transitive Property of Equality, angles BCD and BAD are congruent.Step 6: Angles ABC and BAT are congruent by the Alternate Interior Theorem.(The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.) Step 7: Angles BAT and CDA are congruent by the Corresponding Angles Theorem.Step 8: By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.