The segments AB and CM intersect at point O. It is known that the angle ACO

The segments AB and CM intersect at point O. It is known that the angle ACO is equal to the angle of MBO and CO = BO. Prove that triangle ACO = triangle MBO.

Given two segments AB and CM, intersecting at point O. Connect point A with point C, and point M with point B, and consider the triangles formed on these segments: ΔАСО and ΔМВО. In them, the corresponding sides of CO and BO are equal by condition, the corresponding angles ∠АСО and ∠МВО are also equal by condition. At the intersection of the segments, vertical angles ∠СОА and ∠СОМ were formed. They in the triangles ΔАСО and ΔМВО are corresponding and equal in terms of the property of vertical angles. The triangles under consideration have one equal side and two adjacent corners. It can be concluded that ΔАСО = ΔМВО according to the second sign of equality of triangles.