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Understanding Perpendicular Bisectors: Calculating x and Theorems

Learn the concept of perpendicular bisectors and how to apply it to find the value of x in a geometric scenario. Explore Theorem 5.1 and Theorem 5.2 to understand equidistant points and their relationships. Solve practical examples to enhance your geometrical skills.

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Understanding Perpendicular Bisectors: Calculating x and Theorems

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  1. Week 7 Warm Up 11.28.11 1) What is the value of x? 3x⁰ 28⁰ x⁰

  2. Perpendicular Bisector A segment, ray, line or plane that is perpendicular to a segment at its midpoint. • C midpoint • Ex 1 M A B is a perpendicular bisector. ≅

  3. Equidistant When a point is the same distance from two points. Ex 2 • C • P A B CA = CB

  4. Theorem 5.1 • C A B P If is the perpendicular bisector of then CA = CB.

  5. Theorem 5.2 • C A B P • D If DA = DB, then D is on the perpendicular bisector.

  6. Ex 3 Is Q on ? is perp. bisector of T 12 Q M N 12 S ≅ because is a perp bisector ≅ Perpendicular Bisector Theorem ( 5.1 ) Q is equidistant between T and S Given Q is on the perp bisector of T and S which is

  7. Do 1 : is a perp bisector of . T What is the measure of ? 17 8 Q M N 8 S

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