Triangle HIJ is an isosceles triangle because the base angles opposite of sides HI and HJ are congruent. Therefore, by the Converse of the Isosceles Triangle Theorem, if two base angles are congruent in a triangle, then the sides opposite those base angles are congruent. Now that angles HIJ and HJI are congruent and sides HI and HJ are congruent, triangle HIJ is an isosceles triangle by definition; it has a pair of congruent base angles whose sides opposite of the base angles are congruent.