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Which statement is NOT equivalent to the fifth postulate?

Class 9The Fifth PostulateGeometry — Foundations
  • AA circle can be drawn with any centre and any radius
  • BThere exists a pair of straight lines that are everywhere equidistant
  • CThrough a point not on a line, exactly one parallel can be drawn
  • DThe sum of the angles of a triangle is 180°

Step-by-Step Solution

Drawing a circle with any centre and radius is the THIRD postulate, not related to the fifth. The other three statements are equivalent forms of the fifth postulate.
Answer: A) A circle can be drawn with any centre and any radius

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