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 a triangle AOC and a triangle DOB. Angle AOC = angle DOB as they are vertical. Parties CO = ОD and AO = ОВ by condition. Therefore, 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.