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The Isosceles Triangle Theorems 4.4 Vocabulary of an Isosceles Triangle Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Corollaries •An equilateral triangle is also equiangular •An equilateral triangle has three 60° angles. •The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. One more theorem… If two angles of a triangle are congruent, then the sides opposite those angles are congruent. …and corollary An equiangular triangle is also equilateral.