Question

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

Answer 1

See answer below

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 ≅