Definition

Noun: A triangle in which all three interior angles are acute angles (each measuring less than 90 degrees).

Usage

The term "acute triangle" is used in geometry to classify a triangle based on the measures of its angles. It describes the fundamental property that every angle within the shape is acute.

Examples

• In geometry class, we learned that an acute triangle has all angles smaller than a right angle.
• The architect used an acute triangle as a key design element for the modern facade.
• If every internal angle of a triangle is less than 90 degrees, it is correctly classified as an acute triangle.

Advanced Usage

• "strictly acute triangle": Sometimes used in advanced mathematics to emphasize that no angle is a right angle (90°) or obtuse (>90°), which is inherent in the standard definition of an acute triangle.
• The concept is foundational for theorems and proofs involving inequalities in triangles, such as determining the relationship between sides and opposite angles.

Variants and Related Words

• Acute-angled triangle: A less common but perfectly synonymous term.
• Obtuse triangle: A triangle with one interior angle greater than 90 degrees.
• Right triangle: A triangle with one interior angle equal to 90 degrees.
• Equiangular triangle: A triangle where all three interior angles are equal (each 60 degrees); this is a specific type of acute triangle.

Synonyms

• Acute-angled triangle

Antonyms

• Obtuse triangle
• Right triangle (or right-angled triangle)

Noun

1. a triangle whose interior angles are all acute