5-1+Perpendicular+and+Bisectors

5-1 Perpendicular and Bisectors

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



A point is equidistant from two points if its distance from each point is the same.

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

The Converse of the Perpendicular Bisector Theorem : We can conclude that segment CD is a //perpendicular bisector// of segment AB.
 * If a point is equidistant from the endpoint of a segment, then it is on the perpendicular bisector of the segment.

An Angle Bisector is a ray that divides an angle into two adjacent angles that are congruent.

The Angle Bisector Theorem : If the measure of angle BAD equals the measure of angle CAD, then BD=DC.
 * If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

The Converse of the Angle Bisector Theorem : We can conclude that ray AD is the //angle bisector// of angle BAC.
 * 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.

//__Helpful Links__// [|Perperndicular Bisector and Example] [|McDougal Littell Textbook]