Equidistant - When a point is the same distance from two or more objects
Perpendicular Bisector Theorem - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Theorem - If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
In this diagram, assuming segment AD is congruent to BD, then we can say that points B and A are equidistant from point D. Also, assuming that segment AP is congruent to segment BP, we can say that points B and A are equidistant from point P.
Angle Bisector Theorem - If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
Converse of the Angle Bisector Theorem - If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
Angle Bisector Theorem - in this diagram, since ∠CAD is congruent to ∠BAD, then segment BD and segment DC must be congruent.