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A student claims: 'The fifth postulate can be proved using only the first four postulates of Euclid.'
What is the correct mathematical conclusion reached after about 2000 years of study?

Class 9The Fifth PostulateGeometry — Foundations
  • AIt cannot be proved from the other four; it is independent
  • BIt can be easily proved from the first four
  • CIt contradicts the first four
  • DIt is the same as the first postulate

Step-by-Step Solution

Centuries of attempts failed; the fifth postulate is logically independent of the first four. Replacing it leads to consistent non-Euclidean geometries.
Answer: A) It cannot be proved from the other four; it is independent

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