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  "body": "\n## Summary\n\nAbsolute geometry, also called neutral geometry, is the geometry that [[Hilbert's axioms|KM1FB8XZ2R]] give without the axiom of parallels.\nIts theorems hold both in [[Euclidean geometry|KRZD96GSVC]] and in [[hyperbolic geometry|GN4N94GQ0Z]].\nIt contains the congruence criteria for triangles, the [[exterior angle theorem|0NTSE7EREA]] and the [[Saccheri–Legendre theorem|1Y2XK0QJDX]], but not the angle sum $180^\\circ$.\n\n## Explanations\n\n### L1 human\n\nAbsolute geometry is what remains of school geometry when one forgets the rule about parallel lines.\nEverything proved there is true both on a flat plane and in the curved world of hyperbolic geometry.\nFor example, in any triangle an exterior angle is larger than each of the two opposite interior angles.\nOn the other hand, \"the angles of a triangle add up to $180^\\circ$\" is not a theorem of absolute geometry.\n",
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