# NCERT Class 9 Maths Chapter 5 Introduction to Euclid's Geometry (Latest Edition)

Gurmeet Kaur

Download the NCERT Class 9 Maths Chapter 5 Introduction to Euclid's Geometry in PDF format. With the help of the latest edition of the chapter, students can make preparations for their Maths exam in the right way. We have also provided here the link to download the precise and simple NCERT Solutions for the chapter 5 of Class 9 Maths Book.

About Class 9  Maths Chapter 4 Introduction to Euclid's Geometry

This chapter discusses Euclid’s approach to geometry and helps us correlate this with the present day geometry.

Major topics discussed in the chapter are:

→ Euclid’s Definitions

→ Euclid’s Axioms

→ Euclid’s Postulates

→ Equivalent Versions of Euclid’s Fifth Postulate

A screenshot of the NCERT Class 9 Maths Chapter 5 is given below:

Some important points to revise from the chapter are:

Some of Euclid’s axioms are:

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

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

(5) The whole is greater than the part.

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

(7) Things which are halves of the same things are equal to one another.

Euclid’s five postulates are :

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

Postulate 2 : A terminated line can be produced indefinitely. Postulate 3 : A circle can be drawn with any centre and any radius.

Postulate 4 : All right angles are equal to one another.

Postulate 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.

Two equivalent versions of Euclid’s fifth postulate are:

(i) ‘For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l’.

(ii) Two distinct intersecting lines cannot be parallel to the same line

Try some important questions given below for self assessment:

1. In how many lines two distinct planes can intersect?

2. If a point C lies between two points A and B such that AC = CB then prove that AC= 1/2 AB. Explain with the help of a figure.

3. If C is called the mid-point of a line segment AB. Prove that every line segment has one and only one mid-point.

4. In the given figure, if AC = BD, then prove that AB = CD.

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