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What defines an equilateral triangle?

  1. A triangle with three equal sides and all angles equal to 60 degrees

  2. A triangle with two equal sides and two equal angles

  3. A triangle with sides of different lengths

  4. A triangle with one right angle

The correct answer is: A triangle with three equal sides and all angles equal to 60 degrees

An equilateral triangle is defined by having three sides that are all of the same length. Additionally, because of this property, the angles in an equilateral triangle are also all equal, and specifically, each angle measures 60 degrees. This uniformity in side lengths and angles is what characterizes an equilateral triangle, making option A correct. In contrast, a triangle with two equal sides (described in the second choice) would be classified as an isosceles triangle, not equilateral. The third choice, which describes a triangle with sides of different lengths, refers to a scalene triangle. Lastly, a triangle with one right angle describes a right triangle, which can be isosceles or scalene but does not necessarily have all sides equal. Thus, A is the definition that accurately captures the essence of an equilateral triangle.