Which statement about an equilateral triangle is true?

Which statement about an equilateral triangle is true?

• A. It has two equal sides
• B. All angles are 120 degrees
• C. All three sides are equal and all three angles are equal
• D. It has a right angle

Answer: (C)

The central idea is that an equilateral triangle has both all three sides equal and all three angles equal. When all three sides are the same, each angle opposite those sides must be the same as well, and since the sum of interior angles in any triangle is 180 degrees, each angle in an equilateral triangle is 60 degrees. So the statement that describes both equal sides and equal angles captures exactly what defines an equilateral triangle. The other options miss or contradict these facts: two equal sides describes only an isosceles triangle, three angles of 120 degrees would sum to 360, which isn’t possible in a triangle, and having a right angle would mean the angles aren’t all equal to 60 degrees.

The central idea is that an equilateral triangle has both all three sides equal and all three angles equal. When all three sides are the same, each angle opposite those sides must be the same as well, and since the sum of interior angles in any triangle is 180 degrees, each angle in an equilateral triangle is 60 degrees. So the statement that describes both equal sides and equal angles captures exactly what defines an equilateral triangle. The other options miss or contradict these facts: two equal sides describes only an isosceles triangle, three angles of 120 degrees would sum to 360, which isn’t possible in a triangle, and having a right angle would mean the angles aren’t all equal to 60 degrees.