Lesson 5.2

Use Perpendicular Bisectors

Definitions

• Perpendicular Bisector- Segment, Ray, Line, or Plane that is perpendicular to a segment at its midpoint

• Concurrent- When three or more lines, rays, or segments intersect at the same point(point of concurrency), they are called concurrent lines, rays, or segments.

Theorem 5.2Perpendicular Bisector Theorem

• If CP is the bisector of AB, then CA = CB

A BP

C

If CA = CB, then CP is the bisector of ABTheorem 5.3- Converse Perpendicular Bisector Theorem

Theorem 5.4Concurrency of Perpendicular Bisector

• If PD, PE, and PF are perpendicular bisectors, then PA = PB = PC

B

CA

D E

F

P

Point P is called the Circumcenter