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Perpendiculars and Bisectors I
Perpendicular Bisector ,[object Object],is a  ⊥  bisector of
 
Constructions ,[object Object],[object Object]
Equidistant ,[object Object],[object Object]
 
Theorem: Perpendicular Bisector ,[object Object]
Proof of the Perpendicular Bisector Theorem  Given: Prove: Show ∆ ACP  ≅ ∆ BCP   CA  =  CB ∠ APC  ≅ ∠ CPB Reflexive property of congruence ∆ ACP  ≅ ∆ BCP   SAS Postulate CPCTC CA  =  CB Definition of Congruence Plan: bisects  bisects
Theorem: Perpendicular Bisector Converse ,[object Object],If  DA  =  DB , then  D  lies on the perpendicular bisector of
Prove the Perpendicular Bisector Theorem Converse  Given :  C  is equidistant from  A  and  B Prove :  C  is on the perpendicular bisector of Plan Show ∆ APC  ≅ ∆ BPC   Draw
Example
Homework ,[object Object]

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5.1 perpendiculars and bisectors i

  • 2.
  • 3.  
  • 4.
  • 5.
  • 6.  
  • 7.
  • 8. Proof of the Perpendicular Bisector Theorem Given: Prove: Show ∆ ACP ≅ ∆ BCP CA = CB ∠ APC ≅ ∠ CPB Reflexive property of congruence ∆ ACP ≅ ∆ BCP SAS Postulate CPCTC CA = CB Definition of Congruence Plan: bisects bisects
  • 9.
  • 10. Prove the Perpendicular Bisector Theorem Converse Given : C is equidistant from A and B Prove : C is on the perpendicular bisector of Plan Show ∆ APC ≅ ∆ BPC Draw
  • 12.