Auxiliary lines may be necessary to write the following direct proofs.

**Problem : **

Given: Line PQ is the perpendicular bisector of segment AB.

Prove: Point P is equidistant from points A and B.

**Problem : **

Given:

Segment AB is congruent to segment CB.Prove:

Angle BAD is congruent to angle BCD.

Segment AB is congruent to segment CD.

**Problem : **

Given: Segments TA and TB are tangent segments to circle O.

Prove: Segment TA is congruent to segment TB.

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