If a triangle has all three interior angles equal, what type is it?

If a triangle has all three interior angles equal, what type is it?

• A. Equilateral triangle.
• B. Isosceles triangle.
• C. Right triangle.
• D. Scalene triangle.

Answer: (A)

All three interior angles are equal, so the triangle is equiangular. In any triangle, equal angles face equal sides, so if every angle is the same, every side must be the same length. That combination defines an equilateral triangle. An isosceles triangle has only two equal sides (and thus two equal angles), a right triangle has a 90-degree angle, and a scalene triangle has all sides (and all angles) different. None of those fits when all angles are equal.

All three interior angles are equal, so the triangle is equiangular. In any triangle, equal angles face equal sides, so if every angle is the same, every side must be the same length. That combination defines an equilateral triangle.

An isosceles triangle has only two equal sides (and thus two equal angles), a right triangle has a 90-degree angle, and a scalene triangle has all sides (and all angles) different. None of those fits when all angles are equal.