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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.
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