Construct two angles with parallel sides. (3 cases). Εxamine what applies to the bisectors of these angles.
@Chrisnew, Actually angles do not have "sides".
Definition: An ANGLE is the union of two rays with a common endpoint, called the vertex.
So two angles could have their rays parallel.
Do vertical angles have that property? Think about each point on a line is the endpoint of two rays opposite directions.
I encourage you to follow the advice in reply #2.