CBSE Notes Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

1.0Introduction

Euclid's Geometry was developed by the Greek mathematician Euclid in ancient times and is a basis for classical geometry. This chapter introduces concepts such as points, lines, angles, and Euclid's axioms as stepping blocks toward understanding the principles of geometry and reasoning.

2.0CBSE Class 9 Maths Chapter-5 Introduction to Euclid’s Geometry - Revision Notes

Key  Terms 

Euclid has written definitions of some terms related to geometry in his book Elements. Here are some of the definitions he gives.

1. Point: A point is that which has no part. Meaning it does not have any length, breadth, or thickness.  
2. Line: A line is a one-dimensional figure that is breadthless. 
3. End of the line is also called point.
4. A straight line is a line that lies evenly throughout with points on it.  
5. Surface: The surface is the 2-dimensional figure which has length and breadth but not thickness. Edges of these surfaces are lines. 
6. Plane surface: A surface that lies evenly with straight lines on it. 

3.0Euclid’s Axioms

In maths, there are 7 axioms:  

Axiom-1: Things which are equal to the same thing are equal. 

For Example: Imagine you and your friend are the same age. And your friend’s age is the same as that of her other friend, Sonali. Then your age and Sonali’s age will be the same.

Axiom-2: If equals are added to equals, the whole is equal.

For Example: Imagine you are going to a gym with your brother, and you both lift a weight of 5kg. Then, you both lift 2kg in weight. Then, you both lift a total weight of 7kg.

Axiom-3: If equals are subtracted from equals, the remainders are equal.

For Example: Imagine you and your friend eating 5 cashews daily. One day, you both ate 1 less cashew, and then that day, you both ate 4 cashews each. 

Axiom-4: Things which coincide with one another are equal. 

For Example: Imagine two boxes fit in a spot perfectly. Then, those two boxes are equal in shape and size. Hence, coinciding. 

Axiom-5: The whole is greater than the part.

For Example: Suppose a pizza slice, a pizza will always be greater than the pizza slice in shape, size, and volume. 

Axiom-6: Things that are double of the same things are equal. 

For Example: Imagine that line AB is double the BC and line PQ is double BC. then line PQ = AB. 

Axiom-7: Things that are half of the same things are equal. 

For Example: Imagine Radha’s height is half that of Sonali's. And Yash’s height is half that of Sonali’s. Then Radha’s height is equal to Yash’s height. 

4.0Euclid’s Postulates 

In maths, we have 5 postulates laid by Euclid: 

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

Example: You can draw a straight line between two points on a Map. 

Postulate-2: A terminated line can be produced indefinitely. 

Example: Imagine a road that extends from one village to another, which can further be extended to other places/villages. 

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

Example: By using a compass, you can draw a circle of any radius and with any centre. 

Postulate-4: All right angles are equal. 

 Example: Right angle means 90 degrees angle. So, every right angle is equal, i.e., 90 degrees. 

Postulate-5: If a straight line falling on two different straight lines makes the interior angles on the same side of it taken together smaller than two right angles, then two straight lines, if produced indefinitely, meet on that side where the sum of angles is less than two right angles. (However, if the interior angles are right, making 180 degrees sum, then the two lines are parallel and they will at some point at infinity or not meet at all in an ideal situation.)

Example: Imagine two shores of a river that never meet as they are parallel to each other. In this postulate, in maths, we assume that these parallel lines may meet at some point in infinity. 

5.0Key Features of CBSE Maths Notes for Class 9 Chapter 5

• The content of the notes is ideal for self-learning as it provides examples for a better understanding of axioms and postulates.
• These are aligned with the latest CBSE Curriculum.
• Our expert faculty analysed the notes to ensure their accuracy.