By a similar argument used to prove that AEB ≅ CED,we can show that (AED) ≅ CEB by (SAS) . So, ∠CAD ≅ ∠ (ACB) by CPCTC. Therefore, AD || BC by the converse of the ( ALTERNATE INTERIOR ANGLES) theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram