Geometry (please explain)

Question

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:

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

Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SSS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which statement best describes a flaw in the student's proof?

Answer 1

To prove that a quadrilateral is a parallelogram, you only have to prove that one pair of opposite sides are parallel and congruent. That is given in the diagram.