Right triangle

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

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

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.