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 δbad is congruent to δbcd by the 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