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Isosceles and Equilateral Triangles (4.5) Isosceles Triangle Theorem If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. Anatomy of an Isosceles Triangle Converse of Isosceles Triangle Theorem If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. Theorem 4-5 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Equilateral Triangles Corollary to Theorem 4-3: If a triangle is equilateral, then the triangle is equiangular. Equilateral Triangles Corollary to Theorem 4-4: If a triangle is equiangular, then the triangle is equilateral.