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NCERT Solutions for Class 9 Maths Chapter 5: Introduction To Euclid's Geometry - Exercise 5.2

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NCERT Solutions for Class 9 Maths Chapter 5 (Ex 5.2)

Free PDF download of NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.2 (Ex 5.2) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all NCERT Book Solutions in your emails. Download NCERT Maths Class 9 from Vedantu. Students can also avail of NCERT Solutions Class 9 Science from our website.


Class:

NCERT Solutions for Class 9

Subject:

Class 9 Maths

Chapter Name:

Chapter 5 - Introduction to Euclids Geometry

Exercise:

Exercise - 5.2

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2024-25

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes

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NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2

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

Ans: Euclid’s fifth postulate states that a straight line falling on two another straight lines, will make the interior angle on the same side of it and it is taken together less than two right angles, i.e., ${180^ \circ }$, then, if the two straight lines are being produced indefinitely, then, they will be meeting on that side, where the sum of angles will be less than two right angles.

(Image Will Be Updated Soon)

In other words, it can be represented as:

If, $\angle 1 + \angle 2 < {180^ \circ }$

Then, the lines AB and CD are going to meet at left side of the line PQ.

(Image Will Be Updated Soon)

Now, if $\angle 1 + \angle 2 = {180^ \circ }$

Then the lines AB and CD are not going to intersect each other. And the intersecting line PQ would be perpendicular to lines AB and CD.

Therefore, we can say that the two distinct intersecting lines will not be parallel to the same line.

  1. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Ans: As per Euclid's fifth postulate if a straight line falls on two straight lines and if the interior angles on the same side of that line is less then sum of two right angles then if the two lines are extended indefinitely, then the lines will meet on the side which the sum of the angles is less than two right angles (${180^ \circ }$).

If the sum of interior angles on one side of line is equal to two right angles, then the two lines are said to be parallel lines.

It can be explained from the figures given below:

  • According to Euclid’s 5th postulate, when $n$ line falls on lines $l$ and $m$, and if $\angle 1 + \angle 2 < {180^ \circ }$ , then $\angle 3 + \angle 4 > {180^ \circ }$. Producing line on lines $l$ and $m$ further, they will meet on the side of $\angle 1$ and $\angle 2$ which is less than ${180^ \circ }$.

(Image Will Be Updated Soon)

  • If $\angle 1 + \angle 2 = {180^ \circ }$ , then $\angle 3 + \angle 4 = {180^ \circ }$.

(Image Will Be Updated Soon)

The lines $l$ and $m$, are not going to meet either at the side of $\angle 1$ and $\angle 2$ or at the side of $\angle 3$ and $\angle 4$.

In the above figure, for two the lines $l$ and $m$, sum of interior angles is equal to two right angles (${180^ \circ }$). Hence, they are parallel lines and will not meet each other on either side of line $n$.

  • Therefore, we can say that Euclid’s fifth postulate implies existence of parallel lines.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2

Opting for the NCERT solutions for Ex 5.2 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.2 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 9 students who are thorough with all the concepts from the Subject Introduction to Euclid's Geometry textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 9 Maths Chapter 5 Exercise 5.2 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 9 Maths Chapter 5 Exercise 5.2, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.

Do not delay any more. Download the NCERT solutions for Class 9 Maths Chapter 5 Exercise 5.2 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.

FAQs on NCERT Solutions for Class 9 Maths Chapter 5: Introduction To Euclid's Geometry - Exercise 5.2

1. Explain the Euclid’s Axioms and Postulates used in ncert solutions for class 9 Maths Chapter 5 Introduction to Euclid’s Geometry?

The Axioms and Postulates are the universal truths that do not require proofs. The term axioms and postulates are used interchangeably. The postulates 1 to 4 are simple and obvious and are not to be proved. The most important postulate is the last one.

2. What is the consistency of the system of axioms?

Using the axioms and postulates many theorems have been derived.A system of axioms is called consistent when it is impossible to deduce from these axioms a statement that contradicts any axioms. An axiomatic system is said to be consistent if it lacks contradiction.

3. What are the NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry Exercise 5.2?

In exercise 5.2 there are 2 questions which are based on the fifth postulate. The postulate 5 is usually called the parallel postulate. If a straight line cuts two straight lines makes the interior angles on the same side, if produced indefinately, meet on the same side whose sum is less than 2 right angles.

4. Why is Euclid important in this modern world?

Euclid conceptualize the terms like point, line or plane,etc However these are not accepted by modern mathematicians. Hence this remained undefined. It does not mean that Euclid’s contribution was a waste. The way he used logic and shaped the ideas of western philosophers.

5. How can students solve easily through the ncert solutions provided by vedantu?

Vedantu in-house subject matter experts have solved the questions from the exercise 5.2 with the utmost care and by following all the guidelines by CBSE. With the help of these solutions, they can prepare themselves accordingly for the final exam.