In δabc shown below, ∠bac is congruent to ∠bca: given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. construct a perpendicular bisector from point b to line segment ac. label the point of intersection between this perpendicular bisector and line segment 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 definition of congruent angles. is congruent to line segment dc by δbad is congruent to δbcd by the line segment ab is congruent to line segment bc 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