obtuse triangle
LowFormal, Technical, Academic
Definition
Meaning
A triangle with one angle greater than 90 degrees (but less than 180 degrees).
A geometric figure with three sides where one interior angle exceeds a right angle, making it distinctly different from acute and right triangles in its angular properties.
Linguistics
Semantic Notes
Specifically a mathematical term. Not used metaphorically in general language. Always refers to the angle property, not the side lengths (though side properties follow from the angle).
Dialectal Variation
British vs American Usage
Differences
No substantive differences in meaning or usage. Spelling of 'obtuse' is identical.
Connotations
Purely mathematical, neutral connotations in both varieties.
Frequency
Equal low frequency in both academic and educational contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
Triangle + [is/forms/classifies as] + obtuseObtuse + triangle + [has/contains] + angle > 90°Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Virtually never used.
Academic
Used in geometry, trigonometry, and engineering mathematics courses and textbooks.
Everyday
Rare, only in specific educational or DIY contexts.
Technical
Standard term in mathematics, drafting, architecture, and computer graphics.
Examples
By Part of Speech
adjective
British English
- The triangle is obtuse.
- We need to find the obtuse angle.
American English
- That triangle is obtuse.
- Identify the obtuse angle.
Examples
By CEFR Level
- This shape is an obtuse triangle.
- The triangle has one big angle.
- In the diagram, triangle ABC is an obtuse triangle.
- An obtuse triangle has one angle larger than 90 degrees.
- The law of sines must be applied carefully to obtuse triangles due to the ambiguous case.
- You can identify an obtuse triangle if the square of the longest side is greater than the sum of squares of the other two.
- The trigonometric functions for the obtuse angle in an obtuse triangle are derived using supplementary angle identities.
- In spherical geometry, the classification of triangles as obtuse depends on the sum of their angles exceeding 180 degrees.
Learning
Memory Aids
Mnemonic
Think: 'OBTUSE triangle has one angle that's OBVIOUSLY too big (over 90°).'
Conceptual Metaphor
Not typically used metaphorically. The adjective 'obtuse' alone can metaphorically mean 'slow to understand', but this does not apply to the geometric term 'obtuse triangle'.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct calque from the adjective 'obtuse' (тупой) which primarily means 'dull/blunt' or 'stupid' in everyday Russian. In geometry, the correct term is 'тупоугольный треугольник'.
Common Mistakes
- Confusing it with an acute triangle.
- Thinking all angles are obtuse (only one is).
- Misspelling as 'obtuse angle triangle' (redundant).
Practice
Quiz
Which statement is true for an obtuse triangle?
FAQ
Frequently Asked Questions
No. An equilateral triangle has all angles equal to 60°, so it is acute, not obtuse.
Exactly one. The sum of angles in a triangle is 180°, so if one angle is >90°, the other two must sum to <90°, making them acute.
The side opposite the obtuse angle is always the longest side.
Very rarely. It is a specific geometric term and is not used metaphorically in general English.