# Right triangle

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

A triangle having one interior angle that is a right angle.

mko-right-triangle · definition · v0.5.0



## Mathematical statement

A triangle is called a right triangle if one interior angle equals ninety degrees, equivalently π/2 radians.





## Representative formula (exact TeX)

\gamma=\frac{\pi}{2}





## Assumptions


- The object under discussion is a nondegenerate triangle in the plane.
- Angles are measured in degrees or radians, with 90° and π/2 denoting the same angle.





## Symbol scope


- γ — interior angle designated as the right angle
- π — circle constant





## Intuition, definition, and misconceptions

A triangle can have at most one right angle because its three interior angles sum to 180°.

The side opposite the right angle is the hypotenuse, and the other two sides are the legs. The hypotenuse is the longest side.

A program can check whether three input angles sum to 180° within a tolerance and whether one is 90°, but this remains a check of concrete inputs.

A common mistake is to notice two perpendicular segments without checking that they and a third side form a nondegenerate triangle.





## Adopted derivation guide

[Right triangle: deciding in coordinates which interior angle is right](https://ocme.evemisslab.com/en/derivations/derivation-mko-right-triangle-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites







## Verification boundary

Passing finite angle cases only shows that the reference program matches those tests; it does not complete a formalization of the geometric definition.

not_formalized


- [evidence-sha256-d2f7e95c5eb44099070a59498f1ad1b82c0818327df33683b6e82d8624544ea9](https://ocme.evemisslab.com/data/evidence/d2f7e95c5eb44099070a59498f1ad1b82c0818327df33683b6e82d8624544ea9.json)





## Next obligation

Connect the entry to Mathlib definitions of triangles, angles, and perpendicularity.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/right-triangle.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-right-triangle/index.md)