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Given: RS is the perpendicular bisector of AB
Prove: RA ≅ RB

Given RS Is The Perpendicular Bisector Of AB Prove RA RB class=

Sagot :

Answer:

See answer below

Step-by-step explanation:

RS ⊥ bisector of AB                                   Given

AS ≅ BS                                                       Definition of ⊥ bisector

∠RSB is a right angle                                  Given

∠RSB = 90°                                                  Definition of right angle

∠RSB & ∠RSA form a linear pair                Definition of linear pair  

∠RSB + ∠RSA = 180                                     A linear pair = 180°

   90° +  ∠RSA = 180°                                   Substitution

     ∠RSA =   90                                            Subtraction

   ∠RSB = ∠RSA                                            Substitution            

    ∠RSB ≅ ∠RSA                                         If equal then congruent

   RS ≅   RS                                                  Reflexive

  Δ RAS ≅ ΔRBS                                           SAS

      RA ≅ RB                                                 CPCTC    (corresponding parts of

                                                                                     congruent triangles  ≅

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