# NCERT Solutions for Class 9 Maths Chapter 5

NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.1 and Exercise 5.2 or प्रश्नावली 5.1 and प्रश्नावली 5.2 Euclid’s Geometry in PDF form Hindi Medium and English Medium free to download. All the Question-Answer are based on Current CBSE Syllabus 2019-20 for CBSE Board and UP Board students from 2019-20 onward. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.

 Class 9: Maths – गणित Chapter 5: Euclid’s Geometry ## NCERT Solutions for Class 9 Maths Chapter 5

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### Class 9 Maths Chapter 5 Euclid’s Geometry Solutions

#### Class 9 Maths Exercise 5.1 in English

NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.1 Introduction to Euclid’s Geometry in English Medium free to use ONLINE or download as PDF form to use it OFFLINE. Click here to see Exercise 5.2 or View in Video Format or Hindi Medium solutions. Download Class 9 Maths App for Offline use.  ##### Class 9 Maths Exercise 5.2 in English

NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.2 Euclid’s Geometry in English medium for CBSE and UP Board as well as Gujrat Board (2019 onward). Click here to see Exercise 5.1 or View in Video Format or Hindi Medium solutions. Download Class 9 Maths App for Offline use. #### 9 Maths Chapter 5 Exercise 5.1 in Hindi

NCERT Solutions for Class 9 Maths Chapter 5 प्रश्नावली 5.1 in Hindi Medium based on Latest CBSE Curriculum 2019-2020 free to use. Click here to see प्रश्नावली 5.2 solutions or View in Video Format or English Medium Sols. Download कक्षा 9 गणित App for offline use.  ##### 9 Maths Chapter 5 Exercise 5.2 in Hindi

NCERT Solutions for Class 9 Maths Chapter 5 प्रश्नावली 5.2 in Hindi Medium free to download or use it online free of cost without any login or password. Click here to see प्रश्नावली 5.1 solutions or View in Video Format and English Medium sols. Download कक्षा 9 गणित App for offline use. Visit to Class 9 Maths page or Top of the page

### 9 Maths Chapter 5 Exercise 5.1 & 5.2 Sols in Video

NCERT Solutions for class 9 Maths Exercise 5.1 in video format with complete description. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.

NCERT Solutions for class 9 Maths Exercise 5.2 in video format with complete description.

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##### Important Axioms, Postulates and Terms of Euclid’s Geometry
• Euclid’s Axioms:
• Axiom 1: Things which are equal to the same things, are equal to one another.
• Axiom 2: If equals are added to equals, then the whole are equal.
• Axiom 3: If equals are subtracted from equals, then the remainders are equal.
• Axiom 4: Things which coincide with one another, are equal to one another.
• Axiom 5: The whole is greater than the part.
• Axiom 6: Things which are double of the same things, are equal to one another.
• Axiom 7: Things which are halves of the same things, are equal to one another.

• Euclid’s Postulate:
• 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 center 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.
• Equivalent versions of Euclid’s fifth postulate:
1. ‘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’.
2. Two distinct intersecting lines cannot be parallel to the same line.

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#### Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’?

Axiom 5:
The whole is greater than the part.

Since this is true for anything in any part of the world, this is a universal truth.

#### आप यूक्लिड की पाँचवीं अभिधारणा को किस प्रकार लिखेंगे ताकि वह सरलता से समझी जा सके?

यदि दो रेखाओं को कोई तीसरी रेखा इस प्रकार कटती है कि एक ही ओर बने आंतरिक कोणों का योग 180° से कम हो, तो दोनों रेखाएँ एक दूसरे को प्रतिच्छेद करती हैं।

#### क्या यूक्लिड की पाँचवीं अभिधारणा से समांतर रेखाओं के अस्तित्व का औचित्य निर्धारित होता है? स्पष्ट कीजिए।

हाँ, यूक्लिड की पाँचवीं अभिधारणा से समांतर रेखाओं के अस्तित्व का औचित्य निर्धारित होता है। क्योंकि यदि दो रेखाओं को कोई तीसरी रेखा इस प्रकार कटती है कि एक ही ओर बने आंतरिक कोणों का योग 180° से कम हो, तो दोनों रेखाएँ एक दूसरे को प्रतिच्छेद करती हैं। परन्तु यदि कोणों का योग 180° हो तो रेखाएँ परस्पर प्रतिच्छेद नहीं करती हैं अर्थात समांतर होती हैं।

#### What are the Euclid’s five postulates?

Euclid’s postulates were :
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.

#### What are the equivalent versions of Euclid’s fifth postulate?

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.

#### What are Euclid’s Axioms?

Some of Euclid’s axioms were :
(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.

## 2 thoughts on “NCERT Solutions for Class 9 Maths Chapter 5”

1. Shubham says:

Thanks Sir ji

2. Sumit kumar singh says:

I really very thank you sir g.