1. **Problem Statement:** Given triangle points A, B, C, and D with BC \cong DC and \(m\angle ACB > m\angle ACD\), determine the relationship between segments AB and AD. 2. **Key Information:** BC \cong DC means segments BC and DC are equal in length. 3. **Relevant Theorem:** In a triangle, the side opposite the larger angle is longer. 4. **Apply the theorem:** Since \(m\angle ACB > m\angle ACD\), the side opposite \(\angle ACB\) is longer than the side opposite \(\angle ACD\). 5. **Identify opposite sides:** - Opposite \(\angle ACB\) is side AB. - Opposite \(\angle ACD\) is side AD. 6. **Conclusion:** Since \(m\angle ACB > m\angle ACD\), then \(AB > AD\). **Final answer:** a. AB > AD