In the figure, AC is parallel to MK, OA is the bisector of the angle MOB, BK is the bisector

In the figure, AC is parallel to MK, OA is the bisector of the angle MOB, BK is the bisector of the angle CBO. Prove that AO is parallel to BK

Since, according to the condition, the straight lines AC and MK are parallel, the angle MOB is equal to the angle CBO as criss-crossing angles at the intersection of parallel straight lines AC and MK of the secant OB.

The segments OA and BK are the bisectors of the angles MOB and CBO, and since these angles are equal, then the angle AOB = KBO.

The angle AOB and the angle KBO are cross-lying angles at the intersection of the straight lines OA and BK of the secant OB, and since these angles are equal, the straight lines OA and BK are parallel, which was required to be proved.