The segments AB and CD intersect in their common middle. Prove that lines AC and BD are parallel.

Given:
segment AB,
segment CD,
point O – the point of intersection of segments AB and CD,
CO = OD,
AO = OB.
Prove that lines AC and BD are parallel.
Evidence:
Consider triangle AOC and triangle DOB. Angle AOC = angle DOB as they are vertical. Parties CO = ОD and AO = ОВ by condition. Hence the triangle AOC = DOB. Then the angle ОАС = angle DВО, and they are crosswise for straight lines АС and DB and secant СD, which means АС is parallel to DB. Q.E.D.