NCERT Exemplar Class 9 Maths Chapter 5 Solutions: Introduction to Euclid’s Geometry

NCERT Exemplar Class 9 Maths Solutions Chapter 5 ‘Introduction to Euclid’s Geometry’ will help you build a strong base in the axioms and postulates given by Euclid. You will be able to verify the results with the help of these solutions. In this chapter of NCERT Class 9 Maths Exemplar, there are 4 exercises and 48 problems given in the form of multiple-choice questions, fill in the blanks, long answer questions, and short answer questions. 

The main concepts in this chapter are lines, plane, collinear points, line segments, congruence, the distance between two points, midpoint of a line segment, Euclid’s Axioms and Postulates. You can find all the solutions to the NCERT Exemplar problems of Class 9 Maths Chapter 5 here. These solutions are prepared by our best subject matter experts in an easy to understand manner. 

We always adhere to the latest CBSE guidelines so with the help of these exemplar solutions, you will be able to prepare well for CBSE exams. We also ensure that all the solutions are 100% correct and according to your understanding level. 

Important Topics for NCERT Exemplar Class 9 Maths Solutions Chapter 5: Introduction to Euclid’s Geometry

Basically the word geometry originates from the Greek word geo that means arc and meter in {to measure}. Euclid geometry is a mathematical system that is attributed to Euclid who was the teacher of mathematics in Alexandria in Egypt. Euclid is known as it gave an exceptional idea regarding the concepts of geometry. This chapter of NCERT Exemplar for Class 9 Maths covers different topics that are listed below:

A solid that has a perfect size, shape, position and it can be moved from one place to another place.

  • The boundaries of the solid are known as surfaces. 
  • These boundaries separate one part of the surface from the other part and have no thickness.
  • The surface boundaries are either curves or straight lines 
  • All these lines of the curves end in points.

In the chapter, you will study the definitions of a straight line, surface, plane surface, point, etc. Euclid gave several definitions in the chapter which he divided into 2 types:-

  • axioms 
  • postulates 

He used postulates to describe the assumptions that were specific to geometry whereas on the other hand axioms refer to the assumptions that he use all throughout maths and that is not mainly linked to geometry.

Some of Euclid’s axioms are:-

  • If you add equals to equals, the holes are equals. 
  • If you subtract equals from equals, the remainders come up to be equal.
  • Things that are double of the same things are equal to one another.
  • The whole is always greater than the part.

Also, Euclid also gave 5 postulates in the chapter. Some are listed below.

  • You can draw a straight line from any one point to any other point.
  • You can produce a terminated line indefinitely.
  • All the right angles are equal to one another.

Euclid stated the postulates and axioms that help him to prove some results but on the other hand, he concluded some statements that were totally proved. Euclid calls them propositions or theorems. One of the theorems, states that any two distinct lines can never have more than one point in common. In the chapter, you will know how to prove the theorems in a proper manner.

Exercise Discussions of NCERT Exemplar Class 9 Maths Solutions Chapter 5: Introduction to Euclid’s Geometry

  • Exercise 5.1 consists of 11 questions in which you need to find out the correct answer according to the situation given in that question.
  • Exercise 5.2 consists of 4 questions in which you have to justify your answer if the statement is true or false.
  • Exercise 5.3 has 6 questions in which you are asked to solve the questions making use of appropriate Euclid’s axioms. This exercise identifies that if you have the proper knowledge of different axioms of Euclid.
  • Exercise 5.4 consists of 2 questions in which you need to justify the statements that are given in the questions. This exercise tests your understanding and analytical skills.

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