NCERT Solutions for Class 9 Introduction to Euclid's Geometry Maths Chapter 5 - FREE PDF Download
FAQs on NCERT Solutions Class 9 Maths Chapter 5 Introduction to Euclid's Geometry
1. What are the Main differences between a Postulate and a Theorem? How do the Axioms differ from the Postulates?
Postulate | Theorem |
A postulate is a statement that is accepted true without any proof. | A theorem is a statement which can be proven using postulates, previously proved statements and deductive reasoning. |
It is often called axioms. | It is also called propositions. |
Example: Euclid’s postulates, i.e. A straight line may be drawn by joining anyone point to any other point. | Example: Pythagoras theorem, i.e. In any right-angled triangle, the square of its hypotenuse is equal to the sum of squares of the other two sides. |
The postulates and axioms are often used interchangeably. They differ from each other by the fact that postulates are specific to geometry while, axioms are used throughout mathematics.
2. How many Postulates did Euclid Propose and What are these Postulates?
Euclid proposed five postulates. These five postulates of Euclid are given below:
A straight line may be drawn by joining anyone point to any other point.
A terminated line can be produced indefinitely.
A circle can be drawn of any radius with any centre.
All right angles are equal to one another
If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
3. What are the Other Two Equivalent Versions of Euclid’s Fifth Postulate? What was the Outcome of Attempts to Prove Euclid’s Fifth Postulate?
The other two equivalent versions of Euclid’s fifth postulate are:
For every line l and for every point P not lying on the line, there exists a unique line m which passes through the point P and is parallel to the line l.
Two distinct intersecting lines cannot be parallel to the same given line.
The outcome of attempts to prove Euclid’s fifth postulate using the first four postulates failed. But this led to the discovery of several other geometries, called non-Euclidean geometries. The non-Euclidean geometry is also called spherical geometry. In spherical geometry, lines are not straight. They are parts of great circles.
Euclidean geometry is only valid for the figures in the plane. It fails for the curved surfaces.
4. What is Euclid's Geometry in Class 9?
Euclid’s Geometry, also known as Euclidean Geometry is Chapter 5 of Class 9 Maths and is the study of plane and solid figures based on various axioms and theorems given by the Greek mathematician Euclid. Euclidean geometry deals with the relationship between all these figures. Students can refer to the NCERT Solutions For Class 9 Maths Chapter 5 “Introduction to Euclid’s Geometry” from Vedantu, to help in a better and clear understanding of these concepts.
5. What do we mean by Euclidean Geometry?
The term Geometry comes from the Greek words ‘Geo’, meaning the ‘Earth’, and ‘Metre’, meaning ‘to measure’. The need for the concept of Geometry dates back in time when Greek mathematician Euclid proposed some postulates and axioms that described the relationship and properties of the solid and plane figures. This form of geometry is hence known as Euclidean Geometry. Euclidean geometry is based on Euclid’s ‘Elements,’ which is a mathematical and geometrical book consisting of 13 parts explaining the axioms and postulates.
6. What is the Euclid Axiom?
A proposed statement that declares a certain assumed fact and is generally accepted without any proof is known as an axiom. The Euclidean axiom is also known as the postulates of Euclidean Geometry are the five postulates given by Euclid in the field of Plane Geometry. The axioms are common to entire mathematics whereas the Postulates refer to the assumptions specific to geometry.
7. Are solutions available?
Yes, the solutions for Chapter 5 of Class 9 Maths are easily available on Vedantu. Here, you will find the best possible explanations for this chapter and all your NCERT Solutions for your exercises are provided in PDF format too, which is totally free to download and you can study from it even in the offline mode. For this:
Visit Vedantu
You can select your preferred chapter
Click on the download PDF option.
Once you’re redirected to a page you will be able to download it.
8. Can I score full marks in Chapter 5 Class 9?
Maths is a scoring subject. All you have to do is be consistent and practice regularly. If you face difficulty in solving these problems, then you can refer to Vedantu for help at free of cost. Practising the NCERT Solutions for Chapter 5 of Class 9 Maths from Vedantu will bring perfection and help you score full marks in your examination. With the help of the Vedantu website and the Vedantu app, you will be able to ace your exams.
9. What is covered in Chapter 5 of Euclid Geometry Class 9 Maths?
Chapter 5 of Euclid Geometry Class 9 Maths, titled "Introduction to Euclid's Geometry," covers the fundamental principles of geometry as established by the ancient Greek mathematician Euclid. The chapter includes definitions, axioms, and postulates that form the basis of geometric reasoning and proofs.
10. What type of questions can I expect from Chapter 5 of Euclid's Geometry Class 9 in exams?
Questions from Euclid's Geometry Class 9 Chapter 5 typically involve:
Proving geometric properties using Euclid's postulates and axioms.
Understanding and applying definitions and basic terms.
Logical reasoning based on Euclidean principles.
Solving problems that require constructing figures based on given postulates.
11. Why is studying geometry important in Euclid Geometry Class 9 Maths Chapter 5 Solutions PDF?
Studying Euclid's geometry is important because it forms the foundation of all geometric reasoning and proof techniques. It enhances logical thinking, and problem-solving skills, and provides a historical perspective on the development of mathematical thought.
12. What are Euclid’s five postulates in Class 9 Chapter 5 Maths?
Euclid's five postulates in Class 9 Chapter 5 Maths are:
A straight line segment can be drawn joining any two points.
A straight line can be extended indefinitely in both directions.
A circle can be drawn with any centre and any radius.
All right angles are equal to one another.
If a straight line intersects two straight lines and makes the interior angles on the same side less than two right angles, the two lines will meet on that side when extended.
13. What problems do the solutions address in Chapter 5 Maths Class 9?
The solutions typically cover in Class 9th Maths Chapter 5 problems related to:
Identifying points, lines, and planes in diagrams.
Applying definitions of geometric terms to solve problems.
Recognizing congruent and similar shapes based on their properties.
(Optional) Understanding and applying axioms and postulates in basic geometric proofs.