Chapters
Chapter 2: Polynomials
Chapter 3: Coordinate Geometry
Chapter 4: Linear Equations in two Variables
Chapter 5: Introduction to Euclid's Geometry
Chapter 6: Lines and Angles
Chapter 7: Triangles
Chapter 8: Quadrilaterals
Chapter 9: Areas of Parallelograms and Triangles
Chapter 10: Circles
Chapter 11: Constructions
Chapter 12: Heron's Formula
Chapter 13: Surface Area and Volumes
Chapter 14: Statistics
Chapter 15: Probability
Solutions for Chapter 5: Introduction to Euclid's Geometry
Below listed, you can find solutions for Chapter 5 of CBSE NCERT for Class 9 Maths.
NCERT solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.1 [Pages 85 - 86]
Which of the following statements are true and which are false? Give reasons for your answers
Only one line can pass through a single point.
True
False
There are an infinite number of lines which pass through two distinct points.
True
False
A terminated line can be produced indefinitely on both the sides.
True
False
If two circles are equal, then their radii are equal.
True
False
In the following figure, if AB = PQ and PQ = XY, then AB = XY
True
False
Give a definition for parallel lines. Are there other terms that need to be defined first? What are they, and how might you define them?
Give a definition for perpendicular lines. Are there other terms that need to be defined first? What are they, and how might you define them?
Give a definition for line segment. Are there other terms that need to be defined first? What are they, and how might you define them?
Give a definition for radius of a circle. Are there other terms that need to be defined first? What are they, and how might you define them?
Give a definition for square. Are there other terms that need to be defined first? What are they, and how might you define them?
Consider two ‘postulates’ given below:-
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
If a point C lies between two points A and B such that AC = BC, then prove that Ac = 1/2AB. Explain by drawing the figure.
If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
In the following figure, if AC = BD, then prove that AB = CD.
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
NCERT solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2 [Page 88]
How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Solutions for Chapter 5: Introduction to Euclid's Geometry
NCERT solutions for Class 9 Maths chapter 5 - Introduction to Euclid's Geometry
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Concepts covered in Class 9 Maths chapter 5 Introduction to Euclid's Geometry are Concept for Euclid’S Geometry, Euclid’S Definitions, Axioms and Postulates, Equivalent Versions of Euclid’S Fifth Postulate.
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