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Euclid's fifth postulate guarantees the existence and uniqueness of:

Class 9The Fifth PostulateGeometry — Foundations
  • Aa parallel line through an external point
  • Ba circle through three points
  • Can equilateral triangle on a segment
  • Da right angle

Step-by-Step Solution

In Playfair's equivalent form, the fifth postulate guarantees a unique parallel line through a point not on the given line.
Answer: A) a parallel line through an external point

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