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NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

Edited By Ramraj Saini | Updated on Mar 18, 2024 12:38 PM IST

Introduction to Euclid’s Geometry is the NCERT chapter which deals with axioms and postulates used in geometry. The NCERT Class 9 Maths Chapter 5 Notes covers a outline of the chapter Introduction to Euclid’s Geometry. The main topics covered Introduction to Euclid’s Geometry class 9 notes are the Euclid’s postulates and axioms. Class 9 maths chapter 5 notes also cover the basic equations in the chapter. Introduction to Euclid’s Geometry class 9 notes pdf download contains all of these topics. The relevant derivations are not addressed in the CBSE class 9 maths chapter 5 notes.

This Story also Contains
  1. Introduction To Euclid’s Geometry class 9 notes:
  2. Definitions of Euclid’s
  3. Euclid’s Axioms And Postulates
  4. Equivalent Versions of Euclid’s Fifth Postulate
  5. Significance of NCERT class 9 maths chapter 5 notes

Also, students can refer,

Introduction To Euclid’s Geometry class 9 notes:

Euclid is known as the "Father of Geometry".

He was the one who introduced the method of proving mathematical results by using deductive logical reasoning and the results which have been previously proved.

Definitions of Euclid’s

He gave these ideas in the form of definitions-

1. Anything which does not has a component is called Point.

2. A length without a breadth is called Line.

3. The endpoints of any line are Points which makes it a line segment.

4. If a line lies evenly with the points on itself then it is called A Straight Line.

5. Any object that has length and breadth only is called Surface.

6. The edges of any surface are lines.

7. A plane surface is a surface that lies evenly with straight lines on it.

Euclid’s Axioms And Postulates

Euclid assumed few properties which turned out ‘obvious universal truth’.

Axioms

Some common ideas that are used in mathematics but not directly related to mathematics are called Axioms.

Some of the Axioms are-

1. If the two things are equal to a common thing then these are equal to one another. Let p = q and s = q, then p = s.

2. If equals are added to equals, the wholes are equal. Let p = q and add s to both p and q then the result will be equal, p + s = q + s.

3. If equals are subtracted from equals, the remainders are equal. Let p = q and subtract the same number from both then the result would be the same, p – s = q - s

4. Things which coincide with one another are equal to one another.

5. The whole is greater than the part.

Circle

6. Things which are double of the same things are equal to one another.

The double of the two semicircles

7. Things which are halves of the same things are equal to one another. This is vice versa of the above axiom.

Postulates

The assumptions which are very specific in geometry are called Postulates.

There are five postulates :

1. A straight line may be drawn from any one point to any other point.

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2. A terminated line can be produced indefinitely.

1648027793017

3. A circle can be drawn with any centre and any radius.

1648027791098

4. All right angles are equal to one another.

All right angles are equal to one another.

DCA =DCB =HE =HGF= 90°

5. Parallel Postulate

If there is a line segment that passes through two straight lines while forming two interior angles on the same which gives a sum that is less than 180°, then these two lines will meet with each other in a case extended on the side where the sum of two interior angles is less than two right angles.

1648027793219

If the sum of two interior angles on the same side is 180° then the two lines will be parallel to each other.

1648027792796

Equivalent Versions of Euclid’s Fifth Postulate

1. Play fair’s Axiom

This states that in case you have a line ‘l’ and a point P which doesn’t lie on line ‘l’ then there could be only one line that passes through point P which will be parallel to line ‘l’. No other line could be parallel to the line ‘l’ and pass-through point P.

1648027791744

2. Two distinct intersecting lines cannot be parallel to the same line.

This states that in case two lines are intersecting with each other, then a line parallel to one of them could not be parallel to the other intersecting line.

Significance of NCERT class 9 maths chapter 5 notes

Introduction to Euclid’s Geometry class 9th notes will give a detailed overview of the chapter and get a sense of the main topics discussed.

This NCERT class 9 maths chapter 5 notes is also useful for covering the core themes of the CBSE maths syllabus in class 9 as well as for competitive exams such as VITEEE, BITSAT, JEE Main, NEET, and others.

In offline mode, Class 9 maths chapter 5 notes pdf download can be used to prepare.

NCERT Class 9 Notes Chapter wise

NCERT solutions of class 9 subject wise

NCERT Class 9 Exemplar Solutions for Other Subjects:

Frequently Asked Question (FAQs)

1. Are all the main derivations covered in the class 9th maths chapter 5 notes

N0, all the main derivations are not covered in the NCERT notes for class 9 maths chapter 5. This NCERT note is a brief of the main topics and equations covered in the chapter and can be used for revising the Introduction to Euclid’s Geometry.

2. How important is the chapter for the CBSE board exam and how this class 9 Introduction to Euclid’s Geometry notes would help?

Students can expect 4 to 6 marks questions from the notes for class 9 maths chapter 5 and students can refer this note for the quick revision purpose which would help them to increase their marks.

3. State Euclid’s two axioms.

It is mentioned in Introduction to Euclid’s Geometry class 9 notes 

a. If the two things are equal to a common thing then these are equal to one another.

Let p = q and s = q, then p = s.

b. If equals are added to equals, the wholes are equal.

Let p = q and add s to both p and q then the result will be equal.

p + s = q + s

4. State Euclid’s two postulates.

As given in CBSE class 9 maths chapter 5 notes:

  1. A straight line may be drawn from any one point to any other point.

  2. A terminated line can be produced indefinitely

5. Do we get numerical questions from Introduction to Euclid’s Geometry class 9 notes ?

No, there isn’t such numerical-based question but the questions are reasoning based on the axioms and postulates.

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