Equilateral — Definition, Formula & Examples
Equilateral means having all sides of equal length. An equilateral triangle has three sides that are all the same length and three angles that are all the same size.
A polygon is equilateral if and only if all of its sides are congruent. In the specific case of an equilateral triangle, each interior angle measures exactly , making it both equiangular and equilateral.
How It Works
To check whether a shape is equilateral, measure all of its sides. If every side has the same length, the shape is equilateral. For triangles, you only need to confirm that all three sides match. A useful shortcut: if you know all three angles of a triangle are , the triangle must be equilateral, and vice versa.
Worked Example
Problem: A triangle has sides measuring 5 cm, 5 cm, and 5 cm. Is it equilateral? What is each angle?
Check the sides: All three sides are 5 cm, so every side is the same length.
Find each angle: The angle sum of any triangle is 180°. In an equilateral triangle, all three angles are equal, so divide by 3.
Answer: Yes, the triangle is equilateral, and each angle measures .
Why It Matters
Equilateral triangles appear constantly in tiling patterns, engineering trusses, and road signs. Recognizing them quickly helps you solve problems in geometry courses from elementary school through high school proofs about congruence and symmetry.
Common Mistakes
Mistake: Confusing equilateral with equiangular for all shapes.
Correction: For triangles, equilateral always means equiangular too. But for other polygons, such as a rhombus, all sides can be equal while the angles are not. The two properties only guarantee each other in triangles.