Class 9 NCERT Solutions- Chapter 5 Introduction to Euclid’s Geometry – Exercise 5.2
Last Updated :
02 Sep, 2024
Chapter 5 of the Class 9 NCERT Mathematics textbook, titled “Introduction to Euclid’s Geometry,” delves into the fundamental concepts of Euclidean geometry. This chapter introduces Euclid’s axioms and postulates, which form the basis of geometric reasoning. Exercise 5.2 focuses on applying Euclid’s axioms and postulates to solve problems related to basic geometric principles and reasoning.
NCERT Solutions for Class 9 – Chapter 5 Introduction to Euclid’s Geometry – Exercise 5.2
This section provides detailed solutions for Exercise 5.2 from Chapter 5 of the Class 9 NCERT Mathematics textbook. The exercise includes problems that require applying Euclid’s axioms and postulates to geometric figures and reasoning. Solutions are presented step-by-step to help students understand how to use Euclidean principles to solve geometric problems effectively.
Euclid’s Geometry is a fundamental topic in the mathematics curriculum of Class 9 providing the building blocks for understanding the logical structure and reasoning behind geometric concepts. Chapter 5 “Introduction to Euclid’s Geometry” delves into the basic postulates and axioms established by the ancient Greek mathematician Euclid forming the foundation for the more advanced topics in geometry. Exercise 5.2 specifically focuses on understanding and applying these postulates to solve various problems.
In this article, we will see the NCERT Solutions for Chapter 5: Introduction to Euclid’s Geometry. This article provides thorough solutions for Exercise 5.2 of the chapter.
Question 1: How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Solution:
Euclid’s fifth postulate:
Euclid’s fifth postulate says that 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 the lines 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 tell us about parallel lines.
Parallel lines are the lines which do not intersect each other ever and are always set at a 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.
Therefore, Two distinct intersecting lines cannot be parallel to the same line.
Question 2: Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Solution:
Yes. Euclid’s fifth postulate imply the existence of the parallel lines.
According to Euclid’s fifth postulate when a line x falls on a line y and z such that ∠1+ ∠2< 180°.
Then, line y and line z on producing further will meet in the side of ∠1 arid ∠2 which is less than 180°.
Therefore, we find that the lines which are not according to Euclid’s fifth postulate. i.e., ∠1 + ∠2 = 180°, do not intersect.
Summary
Chapter 5 of the Class 9 NCERT Mathematics textbook, “Introduction to Euclid’s Geometry,” explores Euclid’s axioms and postulates that form the foundation of geometric reasoning. Exercise 5.2 involves applying these axioms and postulates to solve various geometric problems, reinforcing students’ understanding of fundamental geometric principles and reasoning.
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Introduction to Euclid’s Geometry – FAQs
Why is Euclid known as the “Father of Geometry”?
Euclid is known as the “Father of Geometry” because he organized the basic principles of the geometry into a comprehensive logical system in his work “Elements” which laid the groundwork for the modern geometry.
What are Euclid’s postulates?
The Euclid’s postulates are the fundamental assumptions in geometry that are accepted without proof such as “a straight line segment can be drawn joining the any two points.”
How is Euclid’s Geometry relevant to modern mathematics?
The Euclid’s Geometry forms the basis of modern geometric concepts and is essential for the understanding more complex mathematical ideas making it relevant and foundational for the all higher-level mathematics.
What is the significance of Exercise 5.2 in Chapter 5?
Exercise 5.2 helps students apply Euclid’s postulates and axioms reinforcing their understanding and providing the practice in logical reasoning within the geometry.