equiangular triangle
Definition
- Noun:
- A three-sided regular polygon: An equiangular triangle is a triangle in which all three interior angles are equal. Since the angles in any triangle sum to 180 degrees, each angle in an equiangular triangle measures 60 degrees. This property also makes all three sides equal in length, so an equiangular triangle is synonymous with an equilateral triangle.
Usage Examples
- Noun:
- The architect used an equiangular triangle as the base shape for the structure's design.
- In geometry class, we learned that every equiangular triangle is also equilateral.
Advanced Usage
- Mathematical Context: The term is primarily used in formal geometric contexts to emphasize the angular property. It is often introduced alongside the term "equilateral triangle" to demonstrate the equivalence of these properties in triangles.
- The proof hinges on the fact that the triangle is equiangular.
Variants and Related Words
- Equilateral triangle (n): A triangle with all three sides of equal length. This is a direct synonym for an equiangular triangle.
- Regular triangle (n): Another term for an equiangular or equilateral triangle, highlighting it as the regular polygon for three sides.
Synonyms
- Equilateral triangle
- Regular triangle
Related Phrases and Concepts
- Interior angle: An angle inside a polygon.
- Regular polygon: A polygon that is both equiangular (all angles equal) and equilateral (all sides equal).
Noun
-
a three-sided regular polygon
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