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Isosceles Triangles Since an equiangular ∆'s congruent angles number three, both base angles are congruent to the vertex angle. By the Isosceles Triangle Converse, the legs opposite the bases are congruent. Likewise, each leg is congruent to the base. By the transitive property, all sides are equal. Therefore, the triangle is equilateral. PRINT Menu Theorem Page Theorem Page Isosceles Triangles