Class 9 Euclid's Postulates — practice questions with answers
Geometry — Foundations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. How many points are enough to fix (determine) a unique straight line?
A1
B2
C3
DInfinitely many
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Answer: B) 2
Euclid's first postulate: a straight line may be drawn from any one point to any other point. Two distinct points determine a unique line.
2. If a + b = 12 and b = 5, then a = 7. Which Euclid axiom-type idea justifies replacing b by 5?
AThe whole is greater than the part
BEquals subtracted from equals give equals
CAll right angles are equal
DA line has length only
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Answer: B) Equals subtracted from equals give equals
From a + b = 12, subtract the equal quantities b and 5: a = 12 - 5 = 7. This uses 'if equals are subtracted from equals, the remainders are equal'.
3. A surface, by Euclid's definition, has:
ALength only
BLength and breadth only
CLength, breadth and thickness
DNo dimension
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Answer: B) Length and breadth only
Euclid: 'A surface is that which has length and breadth only' — two dimensions, no thickness.
4. A teacher in Pune asks: 'Why can two distinct lines never have two points in common?' The best Euclid-based reason is:
ATwo points determine a unique line, so two common points would make them the same line
BLines have no breadth
CAll right angles are equal
DA circle needs a centre
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Answer: A) Two points determine a unique line, so two common points would make them the same line
If two distinct lines shared two points, then through those two points two different lines would pass, contradicting the uniqueness from Postulate 1. Hence they share at most one point.
5. A student claims: 'Euclid's fifth postulate can be proved as a theorem using the first four postulates.' Which response is mathematically correct?
ATrue; it was proved by Euclid himself
BFalse; it is independent of the first four and cannot be derived from them
CTrue; it follows from the third postulate
DFalse; it is actually a definition
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Answer: B) False; it is independent of the first four and cannot be derived from them
Centuries of attempts showed the fifth postulate is logically independent of the first four; it cannot be proved from them, which is why consistent non-Euclidean geometries exist.