Two line segments, AB and CD, bisect one another at point 0. Prove that the lines AC and BD are parallel.
I suggest you start with the diagram.
Consider triangles OAC and OBD
OA=OB Since 0 bisects AB
OC=OD since o bisects CD
angleBOD=angleAOC Vertically opposite angles
triangle OAC is congruent to triangle OBD Two sides and included angle test.
angle OAC = angle OBC corresponding angles in congruent triangles
Now consider AB as the transversal that cuts the lines AC and BD
angle OAC angle OBC are alternate angles and since they are equal AC must be parallel to BD