Class 9 Introduction to Euclid's Geometry — 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. Which one of these is an AXIOM (common notion)?
- AA circle can be drawn with any centre and any radius.
- BAll right angles are equal.
- CThings equal to the same thing are equal to each other.
- DA straight line can be drawn between any two points.
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Answer: C) Things equal to the same thing are equal to each other.
Universal truth (used in arithmetic, algebra, geometry) → AXIOM. The other three are specific geometry assumptions → POSTULATES.
2. In which famous 13-book work did Euclid organise geometry into a deductive system?
- AThe Elements
- BThe Principia
- CArithmetica
- DThe Almagest
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Answer: A) The Elements
Euclid's 'The Elements' (around 300 BCE) presented geometry as a logical system built from axioms and postulates.
3. How many distinct lines can be drawn through 5 points, no three of which are collinear (two at a time)?
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Answer: A) 10
Choose 2 points from 5: C(5,2) = (5 x 4)/2 = 10 lines.
4. If two interior co-interior angles on the same side of a transversal are 90 degrees each, the two lines are ____.
- AParallel
- BIntersecting on the left
- CIntersecting on the right
- DThe same line
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Answer: A) Parallel
90 + 90 = 180 degrees = two right angles, so the lines do not meet on either side; they are parallel.
5. Two distinct intersecting lines in a plane have exactly how many points in common?
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Answer: B) 1
Two distinct intersecting lines meet in exactly one point; if they shared two, they would be the same line.