1. **State the problem:** Given parallelogram $ABCD$, prove that $\overline{AD} \cong \overline{CB}$ and $\overline{AB} \cong \overline{CD}$. 2. **Recall the given information and construction:** We have parallelogram $ABCD$ and diagonal $\overline{AC}$. 3. **Use properties of parallelograms:** Opposite sides are parallel, so $\overline{AD} \parallel \overline{CB}$ and $\overline{AB} \parallel \overline{CD}$. 4. **Identify congruent angles:** Alternate interior angles formed by the transversal $\overline{AC}$ are congruent: $\angle DCA \cong \angle BAC$ and $\angle CAD \cong \angle ACB$. 5. **Use reflexive property:** $\overline{AC} \cong \overline{AC}$. 6. **Apply ASA congruence criterion:** Triangles $\triangle DCA$ and $\triangle BAC$ are congruent by ASA (Angle-Side-Angle). 7. **Complete the proof:** Since corresponding parts of congruent triangles are congruent (CPCTC), it follows that $\overline{AD} \cong \overline{CB}$ and $\overline{AB} \cong \overline{CD}$. **Answer for Reasoning #7:** Corresponding parts of congruent triangles are congruent (CPCTC).