This document defines key terms related to perpendicular bisectors and angle bisectors in geometry. It defines a perpendicular bisector as a segment, ray, line, or plane that is perpendicular to another segment at its midpoint. It also defines equidistant and presents the perpendicular bisector theorem and its converse. Finally, it defines the angle bisector theorem and its converse regarding equidistance from the sides of an angle.

1. Terms of Endearment Perpendiculars and Bisectors: 5.1

2. Perpendicular Bisector Segment, ray, line or plane that is perpendicular to a segment at its midpoint

3. Equidistant Distance from a point that is equal to a set of points, lines, rays, or planes

4. Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

5. 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

6. Distance from a point to a line The length of the perpendicular segment from the point to the line If a point is the same distance from one line as it is from another line, the point is equidistant from the lines

7. Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

8. Converse of the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle