Euclid’s Geometry is a fundamental concept that forms the basis for much more advanced topics. Therefore, one of the guides to help you understand this concept is NCERT Solutions for Class 9 Maths Chapter 5 – Introduction to Euclid’s Geometry. It is designed by knowledgeable teachers with years of relevant experience. NCERT Solutions is one of the best guides you could adapt for your study needs.

Furthermore, we also update content as prescribed by CBSE. And moreover, solutions are drafted in a way that prioritizes ease-of-learning.

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## NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

Chapter 5 Introduction to Euclid’s Geometry belongs to Unit 4: Geometry. This particular unit

carries 28 marks out of 100. Therefore, it is quite important to ensure that this chapter is studied thoroughly.

The important topics that are covered under this chapter are:

- Euclid’s Definitions
- Axioms and Postulates

## NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

Euclidean Geometry is a system introduced by the Alexandrian-Greek Mathematician Euclid around 300 BC. More than 2,000 years later, the contributions of Euclid still remain valid. It has practical applications in several fields, ranging from engineering to theoretical physics. It even has academic significance and implications in various disciplines of mathematics and science.

Explore how Euclidean Geometry works and discover the various theorems. Find more important NCERT Solutions For Class 9 Maths to help you practice

**List of Excercises**

Excercise 5.1 Solutions – 7 Questions

Excercise 5.2 Solutions – 2 Questions

### Key Features of NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

- Elaborate and detailed content.
- Formulas are highlighted
- Explanations are presented in an easy-to-understand language
- Designed by qualified teachers
- Includes latest questions from the prescribed syllabus
- Extensive analysis of previous year question papers
- Explore additional learning resources such as sample papers and more.

**More to Explore: **NCERT Solutions Class 9

## Frequently Asked Questions on NCERT Solutions Class 9 Maths Chapter 5

### Which of the following statements are true and which are false? Give reasons for your answers.

(i) Only one line can pass through a single point.

(ii)There are an infinite number of lines which pass through two distinct points.

(iii) A terminated line can be produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v)In Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

(i)False

There can be infinite number of lines that can be drawn through a single point. Hence, the statement mentioned is False

(ii)False

Through two distinct points there can be only one line that can be drawn. Hence, the statement mentioned is False

(iii)True

A line that is terminated can be indefinitely produced on both sides as a line can be extended on both its sides infinitely. Hence, the statement mentioned is True.

(iv) True

The radii of two circles are equal when the two circles are equal. The circumference and the centre of both the circles coincide; and thus, the radius of the two circles should be equal. Hence, the statement mentioned is True.

(v)True

According to Euclid’s 1st axiom- “Things which are equal to the same thing are also equal to one another”. Hence, the statement mentioned is True.

### How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Euclid’s fifth postulate: 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.

i.e., the Euclid’s fifth postulate is about parallel lines.

Parallel lines are the lines which do not intersect each other ever and are always at a constant perpendicular distance apart from each other. Parallel lines can be two or more lines.

A: If X does not lie on the line A then we can draw a line through X which will be parallel to that of the line A.

B: There can be only one line that can be drawn through the point X which is parallel to the line A.

### Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note thatthe question is not about the fifth postulate.)

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

For Example:, A cake. When it is whole or complete, assume that it measures 2 pounds but when a part from it is taken out and measured, its weigh will be smaller than the previous measurement. So, the fifth axiom of Euclid is true for all the materials in the universe. Hence, Axiom 5, in the list of Euclid’s axioms, is considered a ‘universal truth.