---
tag: T7G8X5AD5G
kind: concept
name: Ordered geometry
msc: [51G05]
sources:
  - url: https://en.wikipedia.org/wiki/Ordered_geometry
same_as:
  wikidata: Q7100712
  wikipedia: Ordered geometry
---

## Summary

Ordered geometry is the part of geometry that uses only points, lines and the relation of [[betweenness|CE8GX6ADZS]], with no notion of distance, angle or parallel.
Its axioms are the axioms of incidence and order, including [[Pasch's axiom|KJT98G16Y4]].
It is common to [[Euclidean geometry|KRZD96GSVC]], [[absolute geometry|VKFPCSRNDH]], hyperbolic geometry and affine geometry over ordered fields.
Segments, rays, half-planes, convex sets and the inside of a triangle all belong to it.

## Explanations

### L1 human

Ordered geometry asks what one can say about a drawing if one may not measure anything.
One can still say which point lies between which, which side of a line a point is on, and whether a figure is convex.
For example, "the two diagonals of a convex quadrilateral cross each other" is a fact of ordered geometry.