Auxiliary lines may be necessary to write the following direct proofs.
Given: Line PQ is the perpendicular bisector of segment AB.
Prove: Point P is equidistant from points A and B.
Segment AB is congruent to segment CB.
Angle BAD is congruent to angle BCD.
Segment AB is congruent to segment CD.
Given: Segments TA and TB are tangent segments to circle O.
Prove: Segment TA is congruent to segment TB.