In an isosceles triangle ABC with a base AC, bisectors AE and CD are drawn. Prove that ADC = CEA

Since the triangle ABC is isosceles, the angle BAC = BCA.

In an isosceles triangle, the bisectors drawn from the angles at the base are equal, CD = AE. Angle ACD = CAD as half equal angles at the base of the AC.

Then in the triangles ADC and CEA, the AC side is common, CD = CE, the angle ACD = CAE, and then the triangles ADC and CEA are equal in two sides and the angle between them, which was required to be proved.