Question

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 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 c