# NCERT Solutions for Class 9 Maths Chapter 5

NCERT Solutions for Class 9 Maths Chapter 5 Euclid’s Geometry Exercise 5.1 and Exercise 5.2 in English Medium as well as Hindi Medium updated for new academic session 2020-2021 based on new CBSE Curriculum. Download UP Board Solutions for Class 9 Maths Prashnavali 5.1 and Prashnavali 5.2 in Hindi Medium free to use in PDF format for session 2020-2021. Questions are solved by subject experts without any mistake. It will help all the student to understand the concepts of Euclid’s lemma and postulates. All the NCERT Solutions 2020-21 are updated for new academic session for all board, who are following NCERT Books 2020-21.

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## NCERT Solutions for Class 9 Maths Chapter 5

 Class: 9 Maths (English and Hindi Medium) Chapter 5: Euclid’s Geometry

### 9th Maths Chapter 5 Solutions in English & Hindi Medium

NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.1 and 5.2 in Hindi & English Medium free to use ONLINE or download as PDF form to use it OFFLINE. CBSE NCERT Solutions for Class 9 are updated for academic session 2020-21. Visit to Discussion Forum to share your knowledge with the other users.

• ### Study Material

#### Class 9 Maths Exercise 5.1 and 5.2 Solutions in Video

Class 9 Maths Exercise 5.1 Solutions in Video
Class 9 Maths Exercise 5.2 Solutions in Video
##### What are Euclid’s Postulate?

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.

##### Give two Equivalent versions of Euclid’s fifth postulate.

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

#### Important Notes on 9th Maths Chapter 5

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.

### Important Questions on 9th Maths Chapter 5

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.      