1. It is given that AB and CD are congruent. 2. It is given that angle BAD is congruent to angle CDA. 3. By the identity theorem, AD is congruent to itself. 4. Thus, by SAS, triangle DAC and BDA are congruent. 5. Because corresponding parts of corresponding triangles are congruent, CAD is congruent to BDA. 6. Thus, by definition, triangle AED is isosceles.