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About Introduction to Euclid's Geometry — Class 9 CBSE

Study Euclid's definitions, axioms, postulates, and their role in building geometry. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 5). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Introduction to Euclid's Geometry

  • Introduction to Euclid's Geometry: The Foundation
  • Axioms (Common Notions): Self-Evident Truths
  • Postulates: Specific Assumptions for Geometry
  • Definitions and Theorems: Building the Structure
  • Summary and Preparing for Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Introduction to Euclid's Geometry — solved examples for Class 9 CBSE

Example 1easy

According to Euclid's definitions, which of the following best describes a point?
  1. A)A location with length and breadth
  2. B)That which has no part
  3. C)A straight line without ends
  4. D)A magnitude that cannot be divided

Step-by-step solution

  1. Euclid defined a point as 'that which has no part'. This emphasizes its fundamental nature as a position without any dimension.
  2. Other options describe lines, magnitudes, or incorrectly attribute dimensions to a point.

Answer: That which has no part

Example 2medium

According to Euclid, which of the following best describes a point?
  1. A)A point is a line with no breadth.
  2. B)A point is that which has length, breadth, and thickness.
  3. C)A point is that which has no part.
  4. D)A point is a circle with zero radius.

Step-by-step solution

  1. Euclid defined a point as that which has no part, emphasizing its lack of dimension.
  2. It is a fundamental concept in geometry, representing a precise location without size or extent.

Answer: A point is that which has no part.

Example 3hard

Consider the statement: 'The sum of the angles in a triangle is 180°.' In Euclid's original system, this statement would be classified as:
  1. A)An axiom, as it is a self-evident universal truth.
  2. B)A postulate, as it is a specific assumption applicable only to geometry.
  3. C)A definition, as it describes a property of a triangle.
  4. D)A theorem, as it can be proven using axioms and postulates.

Step-by-step solution

  1. Euclid's axioms are general truths applicable in all fields of mathematics. Postulates are specific assumptions made for geometry. Definitions describe the meaning of terms.
  2. The statement 'The sum of the angles in a triangle is 180°' is not self-evident in the same way an axiom is, nor is it a foundational assumption like the parallel postulate. It is a fundamental result that can be derived from other axioms and postulates (particularly the parallel postulate) through a logical proof.
  3. Therefore, it is classified as a theorem.

Answer: A theorem, as it can be proven using axioms and postulates.

Practice questions on Introduction to Euclid's Geometry

  1. Q1.easy

    Which of Euclid's axioms states, 'Things which are equal to the same thing are equal to one another'?
    1. A)First Axiom
    2. B)Second Axiom
    3. C)Third Axiom
    4. D)Fourth Axiom
    Show answer

    Answer: First Axiom

    Hint: This is one of the most fundamental common notions that allows us to equate different quantities if they share a common equal quantity.

  2. Q2.easy

    If equals are added to equals, the wholes are equal. This statement is an example of a/an:
    1. A)Postulate
    2. B)Definition
    3. C)Axiom
    4. D)Theorem
    Show answer

    Answer: Axiom

    Hint: Consider whether this statement is a general truth applicable beyond geometry or specific to geometric figures.

  3. Q3.easy

    Which of the following is Euclid's Postulate 1?
    1. A)A straight line may be drawn from any one point to any other point.
    2. B)All right angles are equal to one another.
    3. C)A terminated line can be produced indefinitely.
    4. D)A circle can be drawn with any centre and any radius.
    Show answer

    Answer: A straight line may be drawn from any one point to any other point.

    Hint: Think about the very first construction possible with points and lines.

  4. Q4.medium

    Euclid's first postulate states that a straight line may be drawn from:
    1. A)Any one point to at least two other points.
    2. B)Any one point to any other point.
    3. C)Any two points to a single point.
    4. D)A single point only.
    Show answer

    Answer: Any one point to any other point.

    Hint: Consider how many points are needed to uniquely define a straight line.

  5. Q5.medium

    If A = B and C = D, then according to a Euclidean axiom, which of the following is true?
    1. A)A - C = B - D
    2. B)A × C = B × D
    3. C)A + C = B + D
    4. D)A / C = B / D
    Show answer

    Answer: A + C = B + D

    Hint: Think about the axiom that deals with adding equal quantities to other equal quantities.

  6. Q6.medium

    Which of the following statements correctly distinguishes between an 'axiom' and a 'postulate' in Euclid's geometry?
    1. A)Axioms are specific to geometry, while postulates are general statements.
    2. B)Axioms are general truths, while postulates are specific assumptions for geometry.
    3. C)Both axioms and postulates are theorems that need to be proven.
    4. D)Axioms are provable statements, while postulates are unprovable definitions.
    Show answer

    Answer: Axioms are general truths, while postulates are specific assumptions for geometry.

    Hint: Recall that axioms are 'common notions' applicable across all fields, whereas postulates are specifically related to geometry.

  7. Q7.hard

    In the figure below, P, Q, R are three points on a line such that Q lies between P and R. If PQ = QR, and also PQ = 5 cm, and SR = 5 cm (where SR is a separate line segment). Which of the following statements MUST be true?
    1. A)PR = SR
    2. B)QR = SR
    3. C)PR = PQ + SR
    4. D)PR = 10 cm
    Show answer

    Answer: QR = SR

    Hint: Focus on the given equalities and use Euclid's axiom about things equal to the same thing.

  8. Q8.hard

    Consider a line segment AB of length 10 units. A point C is located on AB such that AC = 4 units. Which of the following statements is a direct consequence of Euclid's Axiom 'The whole is greater than the part'?
    1. A)AB = AC + CB
    2. B)AC < AB
    3. C)CB = 6 units
    4. D)If D is another point on AB, then AD < AB
    Show answer

    Answer: AC < AB

    Hint: The axiom states that if you have a whole and a part of it, the whole must be larger than the part.

  9. Q9.hard

    According to Euclid's Postulate 1, 'A straight line may be drawn from any one point to any other point.' If you are given only one point P, how many distinct straight lines can be drawn passing through P?
    1. A)Exactly one
    2. B)Exactly two
    3. C)Infinitely many
    4. D)Zero
    Show answer

    Answer: Infinitely many

    Hint: The postulate specifies drawing a line between *two* points. If only one point is given, consider what freedom you have for the second point.

These are 9 of the 60 questions available for Introduction to Euclid's Geometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.