The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal.

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:

Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB . Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which phrase best completes the student's proof?

are congruent by the AAS postulate
are congruent by the ASA postulate
form a pair of alternate interior angles that are congruent
form a pair of vertical angles that are congruent