In an isosceles triangle ABC, the bisectors CK and AM intersect at the point O.

In an isosceles triangle ABC, the bisectors CK and AM intersect at the point O. Prove that the triangle AOK is equal to the triangle COM

Since the triangle ABC is isosceles, then its angles at the base of the AC are equal, then in the triangles AOK and COM the angles KAO and MCO are equal. The AOK angle and the CОМ angle are equal as the vertical angles formed by the intersection of the bisectors CK and AM.

The AOC triangle is isosceles, since its angles at the base of the AC are equal, then AO = CO.

Then the triangles AOK and COK are equal in side and two adjacent angles, as required.