Definition

1. Noun:
   • A triangle containing an obtuse interior angle: An "obtuse-angled triangle" is a polygon with three sides and three angles, where one of the interior angles measures more than 90 degrees but less than 180 degrees.

Usage

• The term "obtuse-angled triangle" is used in geometry to classify a specific type of triangle based on the measure of its angles.
• It is a formal, descriptive term. In less formal contexts, it is often shortened to "obtuse triangle."

Examples

• Noun:
  • In the diagram, the triangle with angles 100°, 40°, and 40° is clearly an obtuse-angled triangle.
  • To determine if it's an obtuse-angled triangle, check if the square of the longest side is greater than the sum of the squares of the other two sides.

Advanced Usage

• Mathematical Property: In an obtuse-angled triangle, the side opposite the obtuse angle is the longest side.
• Ambiguity Note: The term specifically refers to a triangle with obtuse angle. A triangle cannot have more than one obtuse interior angle.

Variants and Related Words

• Obtuse triangle (n): A common synonym for "obtuse-angled triangle."
• Acute-angled triangle (n): A triangle where all three interior angles are less than 90 degrees.
• Right-angled triangle (n): A triangle containing one 90-degree interior angle.

Synonyms

• Obtuse triangle: The most direct synonym.

Antonyms

• Acute triangle / Acute-angled triangle: A triangle with all angles acute (less than 90°).
• Right triangle / Right-angled triangle: A triangle containing a 90° angle.

Noun

1. a triangle that contains an obtuse interior angle