[tex]
\text{Given:} \\
AD = BC \quad \text{and} \quad AD \parallel BC \\
\text{To Prove:} \\
ABCD \text{ is a parallelogram.} \\
\text{Proof:} \\
\begin{array}{ll}
1. & AD = BC \quad \text{(Given)} \\
2. & AD \parallel BC \quad \text{(Given)} \\
3. & \angle DAC = \angle ACB \quad \text{(Alternate Interior Angles Theorem)} \\
4. & \angle DCA = \angle BAC \quad \text{(Alternate Interior Angles Theorem)} \\
5. & \triangle DAC \cong \triangle ACB \quad \text{(SAS Congruence Postulate)} \\
6. & AB \parallel CD \quad \text{(Corresponding Angles Postulate from congruent triangles)} \\
7. & \text{ABCD is a parallelogram} \quad \text{(Opposite sides are equal and parallel)}
\end{array}
[/tex]
