Given: base ∡bac and ∡acb are congruent.. prove: ∆abc is an isosceles triangle.. when completed, the following paragraph proves that line segment ab is congruent to line segment bc making ∆abc 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.. line segment ad is congruent to line segment dc by by the definition