1. By the definition of an angle bisector, because AC bisects BAD, angles 1 and 2 are congruent. 2. Because sides opposite congruent angles are congruent, BC and CD are congruent. 3. AC is congruent to itself by identity. 4. Thus, while the picture is deceiving, ABC is congruent to ACD by SAS. 5. Because CPCTC, AB is congruent to AD. 6. Because CPCTC, BC is congruent to CD. 7. Angle ACB is obtuse, so AB is longer than BC. 8. Thus, by the transitive property, AD is longer than CD.