Class 9 Euclid's Axioms — 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. Who is regarded as the Father of Geometry, whose famous work 'Elements' lays down the axioms used in geometry?
AEuclid
BPythagoras
CAryabhata
DThales
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Answer: A) Euclid
Euclid of Alexandria wrote the 'Elements', organising geometry on a set of definitions, axioms and postulates. He is called the Father of Geometry.
2. Euclid's fifth postulate is also famously known as the:
AParallel postulate
BPoint postulate
CCircle postulate
DRight-angle postulate
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Answer: A) Parallel postulate
The fifth postulate concerns lines meeting when interior angles are less than two right angles; it is equivalent to the parallel postulate.
3. How many planes can pass through three non-collinear points?
A1
B0
C2
D3
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Answer: A) 1
Three points not on the same line determine exactly one plane.
4. A statement that is accepted as true WITHOUT proof and is specific to geometry (not used in all of mathematics) is best called a:
Apostulate
Btheorem
Ccommon notion
Dconjecture
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Answer: A) postulate
Postulates are geometry-specific assumptions accepted without proof. Common notions (axioms) are general to all mathematics; theorems are proved.
5. In a figure, segment XY is divided by two points M and N (in order X, M, N, Y) such that XM = NY. It is also known that the whole XY = 30 cm and MN = 12 cm. Find the length of XM (in cm).
A18
B9
C8
D10
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Answer: B) 9
XY = XM + MN + NY = 30. Since XM = NY, we get 2(XM) + 12 = 30, so 2(XM) = 18, giving XM = 9 cm.