. 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