Bisectors AE and CD are drawn in an isosceles triangle ABC with base AC. Prove that triangle ADC = triangle CEA.

Since the triangle ABC is isosceles, its angles at the base of the AC are equal.

Angle BAC = BCA.

AE and CD are the bisectors of the angles of the triangle ABC, then the angle ACD = ACD / 2, the angle CAE = CAB / 2, then the angle ACD = CAE.

In triangles ADC and CEA, the side AC is common, angle ACE = CAD, angle CAE = ACD, then triangles ADC and СKA are equal in side and two adjacent angles, which was required to be proved.