What is the origin of the word 'hypotenuse'?

It comes from the Greek 'hypoteinousa', meaning 'stretching under' (the right angle).

Can 'hypotenuse' be used for non-right triangles?

No, it is defined specifically for right-angled triangles.

How do you pronounce 'hypotenuse'?

Commonly: hi-POT-uh-noose (UK) or hi-PAHT-uh-noose (US).

Is there a formula for the hypotenuse?

Yes, the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse.

hypotenuse

Low

UK/haɪˈpɒt.ən.juːz/US/haɪˈpɑː.t̬ən.uːs/

Technical/Formal

My Flashcards

Definition

Meaning

The longest side of a right-angled triangle, opposite the right angle.

By extension, the dominant or foundational element in a triadic structure, or the side defining the distance between the two legs in a geometric setup.

Linguistics

Semantic Notes

Used almost exclusively in geometry and mathematics. Rarely used metaphorically, and when it is, the context is typically highly technical or academic.

Dialectal Variation

British vs American Usage

Differences

No lexical or usage differences; standard mathematical term.

Connotations

Identical; purely technical with no cultural or connotative variation.

Frequency

Identical; low frequency outside mathematics education.

Vocabulary

Collocations

strong

length of the hypotenusecalculate the hypotenuseopposite the hypotenuse

medium

measure the hypotenusefind the hypotenuseright triangle's hypotenuse

weak

long hypotenusehypotenuse formulavalue of the hypotenuse

Grammar

Valency Patterns

The hypotenuse of [a right triangle]To calculate/find the hypotenuse

Vocabulary

Synonyms

Neutral

long sidediagonal (in specific contexts)

Weak

opposite side

Vocabulary

Antonyms

leg (of a triangle)cathetus

Phrases

Idioms & Phrases

“None”

Usage

Context Usage

Business

Virtually never used.

Academic

Exclusively used in mathematics, geometry, trigonometry, and related STEM fields.

Everyday

Rare, except when discussing school-level geometry.

Technical

Core term in geometry, engineering, architecture, and physics for calculations involving right triangles.

Examples

By CEFR Level

In a right triangle, the longest side is the hypotenuse.

You can use the Pythagorean theorem to find the length of the hypotenuse.

The architect calculated the roof's slope by determining the hypotenuse of the triangular support.

The vector's magnitude was equivalent to the hypotenuse of the triangle formed by its orthogonal components.

Learning

Memory Aids

Mnemonic

It's a LONG word for the LONGEST side: HYPOtenuse.

Conceptual Metaphor

FOUNDATION/SUPPORT (the hypotenuse is the base upon which the triangle's properties are calculated).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

Avoid confusing with 'гипотенуза' (direct cognate, same meaning). There is no trap; it's a direct loanword.

Common Mistakes

Misspelling as 'hypotonuse' or 'hypothinus'.
Mispronouncing the middle syllable (e.g., /ˈpɒt/ vs /ˈpɑːt/).
Using it to refer to any side of a triangle.

Practice

Quiz

Fill in the gap

In a right-angled triangle, the square of the is equal to the sum of the squares of the other two sides.

Multiple Choice

What is the hypotenuse?

FAQ

Frequently Asked Questions

: It comes from the Greek 'hypoteinousa', meaning 'stretching under' (the right angle).
: No, it is defined specifically for right-angled triangles.
: Commonly: hi-POT-uh-noose (UK) or hi-PAHT-uh-noose (US).
: Yes, the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse.