In the isosceles triangle ABC with the base of the AC, two medians AP and CD are drawn

In the isosceles triangle ABC with the base of the AC, two medians AP and CD are drawn. Prove that triangle ADC and CPA are equal.

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

Segments CD and AP of the bisector of equal angles at the base of the AC, then the angle PAC = DCA.

In triangles ADC and CPA, the AC side is common, angle DAC = PCA, angle PAC = DCA.

Then the triangles ADC and CPA are equal in side and two angles adjacent to it, the first criterion for the equality of triangles, which was required to prove.