Construct a perpendicular bisector from point B to . Label the point of intersection between this perpendicular bisector and as point D: m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector. ∠BDA is congruent to ∠BDC by the definition of congruent angles. is congruent to by _______1________. ΔBAD is congruent to ΔBCD by the _______2________. is congruent to because corresponding parts of congruent triangles are congruent (CPCTC). Consequently, ΔABC is isosceles by definition of an isosceles triangle. Angle-Side-Angle (ASA) Postulate corresponding parts of congruent triangles are congruent (CPCTC) corresponding parts of congruent triangles are congruent (CPCTC) Angle-Side-Angle (ASA) Postulate the definition of a perpendicular bisector Angle-Side-Angle (ASA) Postulate corresponding parts of congruent triangles are congruent (CPCTC) the definition of a perpendicular bisector