To construct a perpendicular bisector, draw a line segment. From each end of the line segment, draw arcs above and below which intersect from each side. Be sure to maintain the same radius on each. Where the arcs intersect above and below, mark points. Connect these two points. This is a perpendicular bisector.
To prove theorems about parallel lines, use angle relationships. For instance, when two parallel lines are cut by a transversal, specific angle are congruent. When these relationships are congruent, you must have parallel lines:
