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If the fifth postulate is replaced so that NO parallel line exists through an external point, the resulting geometry is:

Class 9The Fifth PostulateGeometry — Foundations
  • Aspherical (elliptic) geometry
  • Bordinary plane geometry
  • Ccoordinate geometry
  • DEuclidean geometry

Step-by-Step Solution

On a sphere any two great circles intersect, so no parallels exist; this is elliptic (spherical) non-Euclidean geometry.
Answer: A) spherical (elliptic) geometry

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