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
Therefore, AD is parallel and
equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are
equal and parallel.