In an isosceles triangle, the angles opposite the congruent sides are congruent.
every equilateral triangle is equiangular and all angles are congruent.
if two angles of a triangle are congruent, then the sides opposite those angles are congruent.
every equiangular triangle is equilateral.
in an isosceles triangle, the ray that bisects the vertex angle bisects the base and is perpendicular to it. it is also the altitude to the base.
a point is on the perpendicular bisector of a line segment if and only if it is equidistant from the endpoints of the segment.