Astudent wrote the following sentences to prove that parallelogram abcd has two pairs of opposite sides equal:

for triangles abd and cdb, alternate interior angle abd is congruent to angle cdb because ab and dc are parallel lines. similarly, alternate interior angle adb is equal to angle cbd because ad and bc are parallel lines. db is equal to db by reflexive property. therefore, triangles abd and cdb are congruent by therefore, ab is congruent to dc and ad is congruent to bc by cpctc.

which phrase best completes the student's proof?