- A(i) and (ii)
- B(i) and (iii)
- C(ii) and (iii)
- Donly (iii)
Step-by-Step Solution
Playfair's axiom gives EXACTLY one parallel = at least one (i) AND at most one (ii). Statement (iii) is false in Euclidean geometry.
Answer: A) (i) and (ii)
Consider three statements about a line l and a point P not on l in Euclidean geometry:
(i) At least one line through P is parallel to l.
(ii) At most one line through P is parallel to l.
(iii) No line through P is parallel to l.
Which combination is guaranteed by Euclid's fifth postulate (Playfair form)?
Class 9The Fifth PostulateGeometry — Foundations
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