Question

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

Answer 1

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 BCD 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 form a pair of vertical angles which are congruent. Therefore, AD is parallel and equal 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?

Triangles ABD and BCD are congruent by the SSS postulate.

Triangles ABD and BCD are congruent by the AAS postulate.

Angle DBC and angle ADB form a pair of corresponding angles which are congruent.

Angle DBC and angle ADB form a pair of alternate interior angles for the lines AD and BC.