Last Updated on August 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 |

### 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.

**A terminated line can be produced indefinitely.**

*Postulate 2:***A circle can be drawn with any centre and any radius.**

*Postulate 3:***All right angles are equal to one another.**

*Postulate 4:***(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.**

*Postulate 5:*### Also check

- Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
- Circles Class 9 Case Study Questions Maths Chapter 9
- Quadrilaterals Class 9 Case Study Questions Maths Chapter 8
- Triangles Class 9 Case Study Questions Maths Chapter 7
- Lines and Angles Class 9 Case Study Questions Maths Chapter 6
- Introduction to Euclid’s Geometry Class 9 Case Study Questions Maths Chapter 5
- Linear Equations in Two Variables Class 9 Case Study Questions Maths Chapter 4
- Coordinate Geometry Class 9 Case Study Questions Maths Chapter 3
- Polynomials Class 9 Case Study Questions Maths Chapter 2
- Number Systems Class 9 Case Study Questions Maths Chapter 1

### 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.

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### 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.