**Geometry Chapter 5.1 Perpendiculars and Bisectors**:

**I) Vocabulary:**

**A) Perpendicular Bisectors**- a segment, ray, line or plane that is perpendicular to a segment at its midpoint.

**B) Equidistant**- a point is equidistant from two points if its distance from each point is the same.

**C) Distance from a point to a line**- is defined as the length of the perpendicular segment from the point to the line.

**D) Equidistant from the two lines**- when a point is the same distance from one line as it is from another line.

**II) Theorems:**

**A) Perpendicular Bisector Theorem**- if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

**Example**: If line CP is the perpendicular bisector of line segment AB, then CA = CB.

**B) 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.

**Example:**If DA = DB, then point D lies on the perpendicular bisector of line segment AB.

**C) Angle Bisector Theorem**- if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

**Example:**if measure of angle BAD = measure of angle CAD, then BD = DC.

**D) 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.

**Example**: If DB = DC, then measure of angle BAD = measure of angle CAD