Definition

1. Adjective:

   • Having all sides or faces equal: In geometry, "equilateral" describes a polygon or polyhedron where all sides (for polygons) or all faces (for polyhedra) are of equal length or measure. The most common example is an equilateral triangle.

2. Noun:

   • A figure whose sides are all equal: As a noun, "equilateral" refers to a geometric figure, typically a polygon, that possesses sides of equal length.

Examples of Usage

• Adjective:
  • An equilateral triangle is a fundamental shape in geometry.
  • The architect designed a courtyard in the shape of an equilateral hexagon.
• Noun:
  • The student was asked to calculate the area of the equilateral. (Here, "equilateral" is understood from context, e.g., an equilateral triangle).
  • All equilaterals are also equiangular polygons.

Advanced Usage

• "Equilateral polygon": A polygon with all sides of equal length. This is a more precise term than the noun "equilateral" alone.
  • A square is a common example of an equilateral polygon.
• In a broader mathematical context, the property of being equilateral can be discussed for various shapes.
  • The study focused on the properties of equilateral tetrahedra.

Variants and Related Words

• Equilaterally (adverb): In an equilateral manner.
  • The figure was constructed equilaterally.
• Equilateralness (noun): The state or quality of being equilateral. (This is a rare, technical term).

Synonyms

• Regular (when referring to polygons that are both equilateral and equiangular).
• Equal-sided.

Antonyms

• Scalene (specifically for triangles with no equal sides).
• Irregular (for polygons with sides of differing lengths).

Related Phrases and Concepts

• Equilateral triangle: A triangle with all three sides equal and all internal angles measuring 60 degrees.
  • The formula for the area of an equilateral triangle is (√3/4) * side².
• Equiangular: Having all angles equal. A polygon can be equilateral without being equiangular (e.g., a rhombus), but a triangle that is equilateral is always equiangular.

Adjective

1. having all sides or faces equal

Noun

1. a figure whose sides are all equal