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Understanding Perpendicular Bisectors and Their Concurrency Theorems

Explore the definitions and theorems related to perpendicular bisectors in geometry, including the Perpendicular Bisector Theorem, Converse Perpendicular Bisector Theorem, and Concurrency of Perpendicular Bisector. Understand the significance of concurrent lines, rays, or segments. Discover how the circumcenter plays a key role in the intersection of perpendicular bisectors.

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Understanding Perpendicular Bisectors and Their Concurrency Theorems

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  1. Lesson 5.2 Use Perpendicular Bisectors

  2. 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.

  3. Theorem 5.2Perpendicular Bisector Theorem • If CP is the bisector of AB, then CA = CB C A P B Theorem 5.3- Converse Perpendicular Bisector Theorem If CA = CB, then CP is the bisector of AB

  4. Theorem 5.4Concurrency of Perpendicular Bisector • If PD, PE, and PF are perpendicular bisectors, then PA = PB = PC B Point P is called the Circumcenter D E P C A F

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