Construct a perpendicular bisector from point B to line AC .
Label the point of intersection between this perpendicular bisector and line AC as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the _______1________. line AD
is congruent to line DC by _______2________.
∆BAD is congruent to ∆BCD by the Angle-Side-Angle (ASA) Postulate.
Consequently, line AB is congruent to line BC because congrucongruent parts of congruent triangles are congruent (CPCTC).

Question

Construct a perpendicular bisector from point B to line AC . 
Label the point of intersection between this perpendicular bisector and line AC  as point D. 
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector. 
∡BDA is congruent to ∡BDC by the _______1________. line AD
 is congruent to line DC  by _______2________. 
∆BAD is congruent to ∆BCD by the Angle-Side-Angle (ASA) Postulate. 
Consequently, line AB is congruent to line BC because congrucongruent parts of congruent triangles are congruent (CPCTC).