We have that ab || dc. by a similar argument used to prove that aeb ≅ ced, we can show that ≅ ceb by . so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.

We have that AB || DC.

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

1. AED
2. SAS
3. ACB
4. ALTERNATE INTERIOR ANGLES

Agc and bgd are vertical angles