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

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

Edited By Safeer PP | Updated on Jul 18, 2022 02:14 PM IST

The topic of Euclid's postulate, specifically its fifth postulate, is covered in NCERT Solutions for Class 9 Maths exercise 5.2. Euclid's Geometry is the study of geometry based on undefined words such as points, lines, and planes of flat spaces, which was developed by Euclid, the Father of Geometry. In exercise 5.2 Class 9 Maths, Euclid's Euclid's geometry discussed the shape, size, and position of solid shapes such as the surface, straight or curved lines, points, and so on… Geometrically, there are 5 Euclid’s postulates They are,

This Story also Contains
  1. Introduction To Euclid's Geometry Class 9 Chapter 5 Exercise: 5.2
  2. More About NCERT Solutions for Class 9 Maths Exercise 5.2
  3. Benefits of NCERT Solutions for Class 9 Maths Exercise 5.2

• Postulate -1: A line segment is often drawn for any two given points.

• Postulate -2: A-line segments are often extended in either direction to make a line

• Postulate -3: To explain a circle with any centre and radius, that's a circle that is often drawn with any centre and any radius.

• Postulate -4: All right angles are proportional to one another.

• Postulate -5: If two lines are intersected by a third in such a way that the total of the inner angles on one side is less than two right angles, then the two lines will intersect endlessly on that side.

NCERT solutions for Class 9 Maths chapter 5 exercise 5.2 are made up of two questions that are based on Euclid's fifth postulate. In this Class 9 Maths chapter 5 exercise 5.2, the ideas connected to Euclid's Geometry are thoroughly discussed. Along with NCERT book Class 9 Maths chapter 5 exercise 5.2 the subsequent exercises also are present.

Introduction To Euclid's Geometry Class 9 Chapter 5 Exercise: 5.2

Q1 How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Answer:

Euclid's 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.

1640082956556 Now, in an easy way
Let the line PQ in falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180° on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of PQ.

Q2 Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Answer: 1640082975160 According to Euclid's 5 postulates, the line PQ falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180° on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of the PQ
Now,
If \angle 1+\angle 2 = 180\degree then, the line never intersects with each other.
Therefore, we can say that lines AB and CD are parallel to each other


More About NCERT Solutions for Class 9 Maths Exercise 5.2

Class 9 Maths chapter 5 exercise 5.2, The fifth postulate of Euclid geometry states that if any straight line falling on two straight lines produces interior angles on the same side of it that are less than two right angles when added together, then the two straight lines will meet on the side on which the sum of angles is less than two right angles if produced indefinitely.

Euclid proposed the fifth postulate. John Playfair's most recent version of Euclid's fifth postulate. Provided a line and a point not on it in a plane, he claims that only one line parallel to the given line can be traced through the point. This fifth postulate is commonly referred to as the parallel postulate since it is based on the uniqueness of parallel lines.

Also Read| Introduction To Euclid's Geometry Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Exercise 5.2

• Through NCERT solutions for Class 9 Maths exercise 5.2, we will easily comprehend Euclid’s fifth postulate and these questions will assist us in mastering the principles of Euclid's geometry.

• If we look at the NCERT solution for Class 9 Maths chapter 5 exercise 5.2, we can easily remember all important terms introduced in Euclid’s geometry.

• For solving the questions of exercise 5.2 Class 9 Maths, we need to memorize the definitions and theorems clearly to understand and reinforce their knowledge. This may help gain a deep understanding of this topic.

Frequently Asked Question (FAQs)

1. What is the fifth Euclid's postulate, according to NCERT solutions for Class 9 Maths chapter 5 exercise 5.2 ?

Postulate -5 indicates that if two lines are crossed by a third in such a way that the total of the inner angles on one side is less than two right angles, the two lines will intersect on that side if produced indefinitely, according to NCERT solutions for Class 9 Maths chapter 5 exercise 5.2.

2. The equivalent version of Euclid’s fifth postulate given by __________ .

The equivalent version of Euclid’s fifth postulate was given by John Playfair. 

3. State the Euclid’s fifth postulate which was given by John Playfair.

John Playfair states that in a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.

4. Fifth postulate is popularly known as the __________

The fifth postulate is popularly known as the parallel postulate.

5. According to NCERT solutions for Class 9 Maths chapter 5 exercise 5.2 , why is the fifth postulate popularly known as the parallel postulate?

The fifth postulate is popularly known as the parallel postulate because it has been provided on the basis of the uniqueness of parallel lines. 

6. Who introduced Euclid’s fifth postulate for the first time?

Euclid’s fifth postulate was introduced by Euclid.

7. Euclid is known as the "Father of ______ ."

Euclid, the Father of Geometry, is the answer.

8. According to NCERT solutions for Class 9 Maths chapter 5 exercise 5.2 , define parallel lines.

According to NCERT solutions for Class 9 Maths chapter 5 exercise 5.2 , The lines which never intersect each other and are always at a constant distance perpendicular to each other are known as parallel lines. 

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