Introduction to Euclid’s Geometry Class 9 Case Study Questions Maths Chapter 5

Download CBSE and ICSE Books in PDF Format

Reading Time: 9 minutes

Last Updated on October 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Chapter	Introduction to Euclid’s Geometry
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	9
Subject	Maths
Useful for	Class 9 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 9 Maths Chapterwise Case Study

Customised Study Materials for Teachers, Schools and Coaching Institute

Table of Contents

Case Study Questions on Introduction to Euclid’s Geometry

Questions

A National Public School organised an education trip to a museum. Almost all the students of class IX went to the trip with their teacher of Mathematics. They saw many pictures of mathematicians and read about their contributions in the field of Mathematics. After visiting the museum, teacher asked the following questions from the students.

On the basis of the above information, solve the following questions:

Q 1. Pythagoras was a student of:
a. Euclid
b. Thales
c. Archimedes
d. Both a. and b.

Ans. (b) Pythagoras was a student of Thales.
So, option (b) is correct.

Q 2. Name of the mathematician who is visible in the last picture, is:
a. Euclid
b. Pythagoras
c. Thales
d. None of these

Ans. (a) Euclid mathematician is visible in the last picture.
So, option (a) is correct.

Q 3. Euclid stated that ‘A circle can be drawn with any centre and any radius’, is a/an:
a. definition
b. postulate
c. axiom
d. proof

Ans. (b) Euclid stated that ‘A circle can be drawn with any centre and any radius’ is postulate.
So, option (b) is correct.

Q 4. In which country Thales belong to?
a. Greece
b. Egypt
c. Babylonia
d. Rome

Ans. (a) Thales belongs to Greece Country.
So, option (a) is correct.

Q 5. Which of the following needs a proof?
a. Definition
b. Theorem
c. Axiom
d. Postulate

Ans. (b) Theorem needs a proof.
So, option (b) is correct.

Understanding Euclid’s Geometry

Euclid’s Definitions

A point is that which has no part.
A line is breadthless length.
The ends of a line are points.
A straight line is a line which lies evenly with the points on itself.
A surface is that which has length and breadth only.
The edges of a surface are lines.
A plane surface is a surface which lies evenly with the straight lines on itself.

Statement

A sentence which can be judged to be true or false, e.g., The sum of the angles of a quadrilateral is 360°, is a true statement and a line segment has one end point, is a false statement.

Axioms

The basic facts taken for granted without proof. e.g., A line has infinitely many points.

Theorem

A mathematical statement whose truth has been established (proved)

Euclid’s Axioms

Things which are equal to the same thing are equal to one another.
If equals are added to equals, the wholes are equal.
If equals are subtracted from equals, the remainders are equal.
Things which coincide with one another, are equal to one another.
The whole is greater than the part.
Things which are double of the same things, are equal to one another.
Things which are halves of the same things, are equal to one another.

Postulate: The assumptions which are specific to geometry, e.g., Two points make a line.

Euclid’s Postulates

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: (Parallel Postulate): 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.

Also check

Topics from which case study questions may be asked

History-Geometry in India and Euclid’s geometry
Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems.
The five postulates of Euclid. Showing the relationship between axiom and theorem, for example:
(Axiom) 1. Given two distinct points, there exists one and only one line through them.
(Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

An axiom generally is true for any field in science, while a postulate can be specific on a particular field.

Case study questions from the above given topic may be asked.

Helpful Links for CBSE Class 9 Preparation

Download Customised White Label Study Materials in MS Word Format

We are providing teaching resources to teachers and coaching institute looking for customised study materials in MS word format. Our High-quality editable study material which is prepared by the expert faculties are Highly useful for Teachers, Mentors, Tutors, Faculties, Coaching Institutes, Coaching Experts, Tuition Centers.

Download Product Brochure

Frequently Asked Questions (FAQs) on Introduction to Euclid’s Geometry Case Study

Q1: What is Euclid’s Geometry?

A1: Euclid’s Geometry is a mathematical system attributed to the ancient Greek mathematician Euclid. It is based on a set of definitions, postulates (axioms), and propositions (theorems). This geometry primarily deals with the properties and relations of points, lines, surfaces, and solids in a two-dimensional and three-dimensional space.

Q2: Who was Euclid?

A2: Euclid was a Greek mathematician, often referred to as the “Father of Geometry.” He lived around 300 BCE in Alexandria, Egypt. His most famous work, Elements, is a collection of books that form the foundation of what is now known as Euclidean geometry.

Q3: What are Euclid’s Axioms?

A3: Euclid’s axioms are basic assumptions that are accepted as true without proof. These axioms form the foundation of Euclidean geometry. Some of the key axioms include:
(i) A straight line segment can be drawn joining any two points.
(ii) Any straight line segment can be extended indefinitely in a straight line.
(iii) All right angles are equal to each other.
(iv) A circle can be drawn with any center and any radius.

Q4: What is the difference between an axiom and a theorem in Euclid’s Geometry?

A4: An axiom is a statement accepted as true without proof, serving as a starting point for further reasoning and arguments. A theorem, on the other hand, is a statement that has been proven to be true based on axioms and previously established theorems.

Q5: How did Euclid contribute to the field of geometry?

A5: Euclid’s major contribution to geometry was the systematic organization of geometric knowledge into a logical and rigorous framework. His work, Elements, consists of 13 books that cover a wide range of topics, including plane geometry, number theory, and solid geometry. This work laid the foundation for the study of geometry for centuries.

Q6: Why is Euclid’s Geometry still important in modern mathematics?

A6: Euclid’s Geometry is important because it provides a clear and logical framework for understanding the properties of shapes and spaces. The principles laid out by Euclid are still used as the foundation for many areas of mathematics, including modern geometry, algebra, and calculus.

Q7: Are there any online resources or tools available for practicing Euclid’s Geometry case study questions?

A8: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.