# m333l fall (2).docx - 3.2.8 An equilateral triangle has...

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3.2.8. An equilateral triangle has three congruent sides. Prove that an equilateral triangle is equiangular. In this equilateral triangle, all three sides are congruent: AB BC CA . The Isosceles Triangle Theorem has been proved in class (points D, E, F, G, H, and I are necessary only to prove the Isosceles Triangle Theorem, not the Equilateral). If AB = AC , then, from the Isosceles Triangle Theorem, we know that: ABC ACB . If BA = BC , then, from the Isosceles Triangle Theorem, we know that BCA BAC . If CA = CB , then from the Isosceles Triangle Theorem, we know that CBA CAB . Therefore ABC BCA CAB 3.2.9. Complete the proof of Theorem 3.2.8 by proving the converse of the proven statement. The converse of the proven statement: An equilateral triangle has three congruent angles. Prove that an equiangular triangle is equilateral. .
In this equiangular triangle, all three angles are congruent: ABC BCA CAB . The Isosceles Triangle Theorem has been proved in class (points D, E, F, G, H, and I are