Question

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC. A student 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 SAS postulate. Therefore, AB is congruent to DC and AD is congru