---
tag: 5SJVH0BHJE
kind: concept
name: Saccheri quadrilateral
msc: [51F05, 51M09]
sources:
  - url: https://en.wikipedia.org/wiki/Saccheri_quadrilateral
same_as:
  wikidata: Q138224
  wikipedia: Saccheri quadrilateral
---

## Summary

A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to a common base.
Giovanni Gerolamo Saccheri studied it in 1733 in an attempt to prove the [[parallel postulate|2PC3XY0PYZ]] from the other axioms.
Its two top angles are equal, and they are right in [[Euclidean geometry|KRZD96GSVC]] and acute in [[hyperbolic geometry|GN4N94GQ0Z]].
So it measures how far an [[absolute plane|VKFPCSRNDH]] is from being Euclidean.

## Explanations

### L1 human

Draw a segment as a base, raise two posts of equal length at right angles at its ends, and join the tops of the posts.
On a flat sheet you get a rectangle, so the top angles are right angles.
Saccheri asked whether the top angles could be smaller than right angles without a contradiction.
They can: this happens in hyperbolic geometry, although Saccheri himself believed he had ruled it out.