The figure below shows a parallelogram abcd. side ab is parallel to side dc and side ad is parallel to side bc: a quadrilateral abcd is shown with the two pairs of opposite sides ad and bc and ab and dc marked parallel . the diagonal are labeled bd and ac a student wrote the following sentences to prove that the two pairs of parallel opposite sides of parallelogram abcd are congruent: for triangles abd and cdb, alternate interior angles abd and cdb are congruent because ab and dc are parallel lines. alternate interior angles adb and cbd are congruent because ad and bc are parallel lines. db is congruent to db by the triangles abd and cdb are congruent by asa postulate. as corresponding parts of congruent triangles are congruent, ab is congruent to dc and ad is congruent to bc by cpctc.
associative property
reflexive property
substitution property
transitive property