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The base angles of an isosceles triangle are congruent. The vertex angle of an isosceles triangle is not necessarily congruent to the base angles.
Vertex angle
-- An isosceles triangle has two equal sides. -- An isosceles triangle has two equal angles. -- An isosceles triangle has two equal interior-angle bisectors. -- The bisector of the vertex angle of an isosceles triangle is also the perpendicular bisector of the triangle's base.
The base
The two "base" angles.