Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry – Exercise 5.1 NCERT Solutions
Introduction
Exercise 5.1 introduces Euclid’s Geometry, the foundation of mathematics. Euclid defined basic terms like point, line, and plane, and established postulates and axioms that form the basis of geometry.
Key Concepts
Point: That which has no part.
Line: Breadthless length.
Surface: That which has only length and breadth.
Postulates: Assumptions accepted without proof (e.g., a straight line can be drawn joining any two points).
Axioms: Self‑evident truths (e.g., things equal to the same thing are equal to one another).
Solved Questions (Step by Step)
Q1. Define a point according to Euclid.
Solution: A point is that which has no part.
Q2. Define a line according to Euclid.
Solution: A line is breadthless length.
Q3. Define a straight line according to Euclid.
Solution: A straight line lies evenly with the points on itself.
Q4. Define a surface according to Euclid.
Solution: A surface has only length and breadth.
Q5. Define the edge of a surface.
Solution: The edge of a surface is a line.
Q6. State Euclid’s first postulate.
Solution: A straight line may be drawn from any point to any other point.
Q7. State Euclid’s second postulate.
Solution: A terminated line can be produced indefinitely.
Q8. State Euclid’s third postulate.
Solution: A circle can be described with any centre and radius.
Q9. State Euclid’s fourth postulate.
Solution: All right angles are equal to one another.
Q10. State Euclid’s fifth postulate.
Solution: If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side.
Q11. State Euclid’s first axiom.
Solution: Things equal to the same thing are equal to one another.
Q12. State Euclid’s second axiom.
Solution: If equals are added to equals, the wholes are equal.
Q13. State Euclid’s third axiom.
Solution: If equals are subtracted from equals, the remainders are equal.
Q14. State Euclid’s fourth axiom.
Solution: Things which coincide with one another are equal to one another.
Q15. State Euclid’s fifth axiom.
Solution: The whole is greater than the part.
FAQs (10 for Exercise 5.1)
Q: Who is Euclid? A: Euclid is known as the “Father of Geometry.”
Q: What is the difference between postulates and axioms? A: Postulates are assumptions specific to geometry; axioms are universal truths.
Q: Why are Euclid’s definitions important? A: They form the foundation of geometry.
Q: What is Euclid’s fifth postulate also called? A: The parallel postulate.
Q: What is an example of an axiom? A: The whole is greater than the part.
Q: Are Euclid’s postulates still used today? A: Yes, they are the basis of classical geometry.
Q: What is the difference between a line and a line segment? A: A line extends indefinitely; a line segment has fixed endpoints.
Q: What is the difference between a postulate and a theorem? A: A postulate is assumed true; a theorem is proved.
Q: Why is Euclid’s geometry called axiomatic? A: Because it is based on axioms and postulates.
Q: What is the significance of Euclid’s work? A: It systematized geometry and influenced mathematics for centuries.
Conclusion
Exercise 5.1 has 15 questions that introduce Euclid’s definitions, postulates, and axioms. This chapter lays the groundwork for understanding geometry logically and systematically.
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