Mathematics is a subject that deals with numbers, shapes, objects, diagrams, graphs and various functions and patterns. Basically, it helps students to develop the reasoning and thinking abilities required in this fast-paced world. Hence, it is quite a demanding subject in almost all fields of sciences and commerce.
Euclid was a Mathematics teacher from Egypt who formulated some of the important concepts of Geometry. Hence in his honour, the Chapter 5 of Class 9 Mathematics is named as Introduction to Euclid’s Geometry. The terminologies and the points covered in this chapter include introduction, definitions, axioms and postulates.
In our NCERT Solutions for Class 9 Mathematics Chapter 5, you will find some of the important definitions listed by Euclid. It also has the various postulates given by Euclid and his understanding of the role of Geometry in Mathematics. His overview on dealing with various geometrical concepts is also included in it.
You can get a detailed analysis of the chapter along with what concepts to study more in-depth on our Extramarks website. You will learn how to study smartly, how to manage time efficiently, and how to draw quick conclusions if you regularly visit Extramarks website and take full advantage of it.
Key Topics Covered In NCERT Solutions for Class 9 Mathematics Chapter 5
The term ‘Geometry’ originates from the Greek word. ‘Geo’ means ‘earth’ whereas ‘metry’ means ‘to measure’. In short, Geometry is the study of the measurement of the earth and various components associated with it. As the name of the chapter suggests, the chapter will be more about Euclid’s understanding of the measurement of earth.
In order to understand this chapter and remember all the definitions and postulates easily, we have provided well-structured academic notes in our NCERT Solutions for Class 9 Mathematics Chapter 5 on the Extramarks’ website. Apart from Class 9 Mathematics solutions, you can also find a lot of material related to Class 9 and other classes for Mathematics as well as other subjects. You can access and take full benefits by registering on our Extramarks’ website.
In our NCERT Solutions for Class 9 Mathematics Chapter 5, we have covered the following topics related to the chapter Introduction to Euclid’s Geometry:
| Exercise |
Topic |
| 5.1 |
Introduction |
| 5.2 |
Euclid’s Definitions, Axioms and Postulates |
| 5.3 |
Equivalent versions of Euclid’s Fifth Postulate |
The definitions and postulates covered in this chapter will go a long way in understanding Geometry as an individual subject and its application in various science and engineering fields. Hence, it is considered a crucial topic.
5.1 Introduction
This section starts with the basic introduction of Geometry, its meaning, where is the word derived from, and its application in day to day life.
You can find the area of regular and irregular shapes, measure the length of the river etc. if you have an idea of the basic applications of Geometry. The different styles of examples based on ancient India help you to grasp these concepts quickly.
Moreover, you will also read about Euclid, a teacher of Mathematics, in this section and try to develop Euclid’s thinking as well as understanding.
5.2 Euclid’s Definitions, Axioms and Postulates
A solid figure has shape, size and well-defined boundaries which can be shifted from one place to another, called surfaces. Each surface has dimensions. Euclid summarised these dimensions into properly structured statements known as definitions.
Further, he gave certain general notions called axioms and stated a few assumptions known as postulates.
The five postulates given by Euclid as given in our Class 9 Mathematics Chapter 5 Solutions are:
Postulate No. 1: A straight line may be drawn from any one point to any other point
Postulate No. 2: A terminated line can be produced indefinitely.
Postulate No. 3: A circle can be drawn with any centre and radius.
Postulate No. 4: All right angles are equal to one another.
Postulate No. 5: 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.
5.3 Equivalent versions of Euclid’s Fifth Postulate
Euclid’s Fifth Postulate is considered one of the most important postulates in the study of Geometry. Due to various uses in the applications of Geometry, it holds a huge significance.
You will find different results and their interpretations associated with it in our NCERT Solutions for Class 9 Mathematics Chapter 5 in detail and develop a solid conceptual understanding.
NCERT Solutions for Class 9 Mathematics Chapter 5 Exercise & Solutions
To get through examinations, be they related to your school or any other competitive examinations, you should regularly solve all the questions and exercises given in the NCERT textbooks to test your knowledge on the topic. Hence, in our NCERT Solutions for Class 9 Mathematics Chapter 5, we have compiled all the questions and solutions in one place to provide you with ease. You can get it on the Extramarks website and test your preparation.
You can find for exercise specific questions and solutions for NCERT Solutions for Class 9 Mathematics Chapter 5 by referring to the following links:
- Chapter 5: Exercise 5.1 Question and answers
- Chapter 5: Exercise 5.2 Question and answers
Along with NCERT Solutions for Class 9 Mathematics Chapter 5, students can explore NCERT Solutions on our Extramarks website for all primary and secondary classes.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT solutions Class 10
- NCERT solutions Class 11
- NCERT solutions Class 12
NCERT Exemplar for Class 9 Mathematics
NCERT Exemplar Class 9 Mathematics book has a compilation of all the advanced level questions designed as per NCERT textbooks based on the latest CBSE syllabus. Questions are made in a way which requires students to use their comprehension skills.
The trend of questions follows the pattern of the competitive examinations. As a result, students rely a lot on NCERT Exemplar for their studies and use it as a reference book in preparation for the competitive examinations. From developing an interest in the subject to gaining insights into learning various concepts of Mathematics, the book offers multiple benefits. Hence, it is fruitful for the students of all the classes irrespective of their curriculum.
Students develop more practical and logical thinking after referring to NCERT Solutions and NCERT Exemplar. It has the key aspect of anything you study helps in better understanding of the things. As a result, students can solve more advanced and higher-level conceptual questions easily. NCERT Exemplar can boost your performance to a great extent and therefore we highly recommend you to incorporate it in your study material.
Key Features of NCERT Solutions for Class 9 Mathematics Chapter 5
The best performers are those who practice a lot and rectify their mistakes. Hence, NCERT Solutions for Class 9 Mathematics Chapter 5 offers a complete guide to everything that is required in your preparation. The key features are provided:
- You can find all the exercises related to question coverage as well as extra questions in our NCERT study material.
- You will learn to apply the use of all the core concepts and will connect them to all the interrelated topics with the help of Extramarks NCERT solutions.
- After completing the NCERT Solutions for Class 9 Mathematics Chapter 5, you will develop confidence in solving Geometry based questions and hence will be able to solve them with ease.