In an isosceles triangle ABC with base AC, bisectors AP and CK are drawn. Prove that APC and CKA are equal.

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

Angle BAC = BCA.

AR and СK are the bisectors of the angles of the triangle ABC, then the angle ACK = ACK / 2, the angle CAP = CAB / 2, then the angle ACK = CAP.

In triangles СKA and APC, the AC side is common, the angle ACP = СAK, the angle CAP = ACK, then the triangles СKA and APC are equal in side and two adjacent angles, the second sign of the equality of triangles, which was required to be proved.