Introduction to Euclid's Geometry — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 10
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 10, "Introduction to Euclid's Geometry". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Introduction to Euclid's Geometry", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Introduction to Euclid's Geometry, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Introduction to Euclid's Geometry (Class 9 Mathematics)
Euclid built geometry from a small set of undefined terms, definitions, axioms and postulates, deducing everything else. This chapter examines that structure, the difference between axioms and postulates, and how questioning the fifth postulate produced non-Euclidean geometries.
- Euclid's Elements
- The thirteen-volume work in which Euclid organised the geometry of his time into a single deductive system from a few starting assumptions.
- Axiom
- A self-evident assumption used throughout mathematics, not specific to geometry — for example, things equal to the same thing are equal to one another.
- Postulate
- An assumption specific to geometry, such as the claim that a straight line may be drawn from any point to any other point.
- Theorem
- A statement proved by logical reasoning from the axioms, postulates and previously proved theorems.
Introduction to Euclid's Geometry — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
According to Euclid, a point is that which has:
A.No part (no dimension)✓ CorrectB.Only lengthC.Length and breadthD.Length, breadth and heightAnswer: A. No part (no dimension)
Explanation: Euclid's first definition: a point is that which has no part — zero dimensions. It marks a location only, with no length, breadth, or thickness, unlike a line (1D) or surface (2D).
- Q2Easy
Through two distinct points, how many straight lines can be drawn?
A.NoneB.Exactly twoC.Infinitely manyD.Exactly one✓ CorrectAnswer: D. Exactly one
Explanation: Euclid's first postulate: through any two distinct points, exactly one straight line can be drawn — never two, never none. This uniqueness is what makes 'the line through A and B' meaningful.
- Q3Easy
Which of the following is one of Euclid's common notions (axioms)?
A.Two parallel lines never have a transversalB.All angles in a triangle sum to 180°C.A circle has 360° at the centreD.Things which are equal to the same thing are equal to one another✓ CorrectAnswer: D. Things which are equal to the same thing are equal to one another
Explanation: Euclid's first common notion is transitivity of equality: things equal to the same thing are equal to one another. If A = C and B = C, this axiom lets us conclude A = B.
- Q4Easy
Which of the following mathematicians proposed non-Euclidean geometry by changing the fifth postulate?
A.Euclid and PythagorasB.Thales and ArchimedesC.Descartes and NewtonD.Lobachevsky and Riemann✓ CorrectAnswer: D. Lobachevsky and Riemann
Explanation: Lobachevsky developed hyperbolic geometry and Riemann developed elliptic geometry, each by replacing Euclid's fifth postulate with a different rule about parallel lines. Pythagoras and Newton never touched the fifth postulate.
- Q5Easy
In Euclid's geometry, a line is defined as a breadthless:
A.SurfaceB.Length✓ CorrectC.PointD.VolumeAnswer: B. Length
Explanation: Euclid's second definition: a line is breadthless length — it extends in only one direction. Confusing it with a surface, which also has breadth, is the common slip.
- Q6Easy
Euclid's third postulate states that a circle can be drawn with any:
A.Three pointsB.Centre and any radius✓ CorrectC.Diameter onlyD.Two parallel linesAnswer: B. Centre and any radius
Explanation: Euclid's third postulate: a circle can be drawn with any point as centre and any distance as radius. Centre and radius are free choices, not fixed to three points or a given diameter.
- Q7Medium
Euclid defined a straight line as one that 'lies evenly with the points on itself'. What does this mean geometrically?
A.A line can be curved at its endsB.A line passes through only two pointsC.A line has a fixed finite lengthD.All points on the line are collinear — the line does not deviate to either side✓ CorrectAnswer: D. All points on the line are collinear — the line does not deviate to either side
Explanation: Euclid's phrase 'lies evenly with the points on itself' describes straightness: every point on the line stays on the same path, never deviating to either side. It describes collinearity, not length or endpoints.
- Q8Medium
Playfair's axiom, which is equivalent to Euclid's fifth postulate, states that:
A.No parallel line can be drawn through a point outside a given lineB.Through a point not on a line, infinitely many parallels can be drawnC.Through a point not on a line, exactly one line parallel to the given line can be drawn✓ CorrectD.Two parallel lines always intersect at infinityAnswer: C. Through a point not on a line, exactly one line parallel to the given line can be drawn
Explanation: Playfair's axiom, equivalent to the fifth postulate, states that through a point not on a line, exactly one parallel to that line can be drawn — not zero, and not infinitely many, in Euclidean geometry.
- Q9Medium
What is the key distinction between Euclid's axioms (common notions) and postulates?
A.Axioms are specific to geometry; postulates apply to all sciencesB.Axioms involve numbers only; postulates involve shapes onlyC.Postulates can be proved; axioms cannotD.Axioms are universal truths for all mathematics; postulates are specific to geometry✓ CorrectAnswer: D. Axioms are universal truths for all mathematics; postulates are specific to geometry
Explanation: Euclid's common notions (axioms) are self-evident truths used across all of mathematics, while his postulates are assumptions specific to geometry alone. The distinction is scope, not which one needs proof — neither does.
- Q10Medium
On a spherical surface, the sum of angles of a triangle is:
A.Exactly 180°B.Less than 180°C.Exactly 90°D.Greater than 180°✓ CorrectAnswer: D. Greater than 180°
Explanation: On a sphere, Riemann's elliptic geometry applies, where a triangle's angle sum exceeds 180° because the surface curves outward. A triangle with the North Pole and two equatorial points can even have three right angles, summing to 270°.
- Q11Medium
According to Euclid, the boundaries of solids are:
A.LinesB.Surfaces✓ CorrectC.PointsD.VolumesAnswer: B. Surfaces
Explanation: Euclid's definition places surfaces as the boundaries of solids, just as points bound lines and lines bound surfaces — each dimension is bounded by the one below it, never directly by a line or a point.
- Q12Hard
Euclid defined a point as 'that which has no part' and a line as 'breadthless length'. Modern mathematicians criticize these as circular or inadequate. Why?
A.Because these definitions are only valid in three dimensionsB.Because points and lines were already defined by PythagorasC.Because 'length' and 'part' themselves need to be defined, creating an infinite regress of definitions✓ CorrectD.Because the definitions contradict the postulatesAnswer: C. Because 'length' and 'part' themselves need to be defined, creating an infinite regress of definitions
Explanation: Euclid's definitions of point and line rely on words like 'part' and 'length' that themselves need defining, creating an endless chain. Modern axiomatic geometry avoids this by treating point, line, and plane as undefined primitive terms.
- Q13Hard
A student argues: 'If two lines are both perpendicular to a third line, they must be parallel.' Which of Euclid's postulates/axioms most directly supports this conclusion in Euclidean geometry?
A.Postulate 1: Two points determine a unique lineB.Postulate 4 (all right angles equal) combined with the converse of the fifth postulate✓ CorrectC.Axiom 8: The whole is greater than the partD.Postulate 3: A circle can be drawn with any centre and radiusAnswer: B. Postulate 4 (all right angles equal) combined with the converse of the fifth postulate
Explanation: If l and m are each perpendicular to n, both make 90° with it. Postulate 4 makes those angles equal, so co-interior angles sum to 90°+90°=180° — the boundary case where the fifth postulate does not force a meeting, so l and m stay parallel.
- Q14Hard
Given: AB = CD, EF = CD, and GH = 2·AB. Using Euclid's axioms, which is true?
A.GH = EFB.GH = CD/2C.GH = 2·EF✓ CorrectD.GH = AB + EFAnswer: C. GH = 2·EF
Explanation: Since AB = CD and EF = CD, transitivity gives AB = EF. Then GH = 2·AB = 2·EF follows from the axiom that doubles of equal things are equal — GH equals twice EF, not EF alone or half of CD.
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Start this chapter free →Introduction to Euclid's Geometry — FAQs
What are the key concepts in Class 9 Mathematics Introduction to Euclid's Geometry?+
Euclid built geometry from a small set of undefined terms, definitions, axioms and postulates, deducing everything else. This chapter examines that structure, the difference between axioms and postulates, and how questioning the fifth postulate produced non-Euclidean geometries. Key ideas include Euclid's Elements, Axiom, Postulate, Theorem.
What does Class 9 Mathematics Chapter 10 (Introduction to Euclid's Geometry) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Introduction to Euclid's Geometry": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Introduction to Euclid's Geometry" questions free to practise?+
Yes. Sign in with Google to practise "Introduction to Euclid's Geometry" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Introduction to Euclid's Geometry" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Introduction to Euclid's Geometry" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Introduction to Euclid's Geometry" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Introduction to Euclid's Geometry (Class 9 Mathematics)?+
The questions that matter most test Euclid's Elements, Axiom, Postulate, Theorem. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Introduction to Euclid's Geometry?+
Yes — Class 9 Mathematics Introduction to Euclid's Geometry has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.