Equivalent Versions of Euclid's Fifth Postulate MCQs
Practice Equivalent Versions of Euclid's Fifth Postulate multiple-choice questions from Introduction to Euclid's Geometry (Class 9 Maths) - tap an answer for instant feedback and a step-by-step solution. Practice the full set free on the RankByte app.
Equivalent Versions of Euclid's Fifth PostulateQuiz - Solve & Score
Q1. Consider the following statements: (I) Playfair's axiom gives exactly one parallel through an external point. (II) Playfair's axiom is equivalent to Euclid's fifth postulate. (III) The fifth postulate can be proved from the first four. Which of the above statement(s) is/are correct?
- A.Only I and II
- B.None of these
- C.Only I
- D.Only III
Answer: A. Only I and II
Q2. Which is an equivalent version of Euclid's fifth postulate?
- A.Playfair's axiom
- B.All right angles are equal
- C.A point has no part
- D.The whole is greater than the part
Answer: A. Playfair's axiom
The core fact here is - Playfair's axiom is the well-known equivalent. That fits the listed correct option directly - Correct. Quickly on the wrong ones: option B) 'All right angles are equal' doesn't hold - That is the fourth postulate; option C) 'A point has no part' misses the point - That is a definition. Hence the answer is A) Playfair's axiom.
Q3. Through a point not on a line, how many lines parallel to it can be drawn in Euclidean geometry?
- A.Exactly one
- B.None
- C.Exactly two
- D.Infinitely many
Answer: A. Exactly one
Going back to the NCERT chapter, Playfair's axiom: exactly one parallel. That fits the listed correct option directly - Correct. Looking at the others: option B) 'None' is wrong because Playfair's axiom guarantees one parallel; option C) 'Exactly two' fails since There is exactly one. Hence the answer is A) Exactly one.
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