Introduction to Euclid’s Geometry Class 9 Assertion Reason Questions Maths Chapter 5

Q: Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies: Understand Each Statement Separately: Determine if each statement is true or false independently. Analyze the Relationship: If both statements are true, check if the reason correctly explains the assertion.

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

Chapter	Introduction to Euclid’s Geometry
Type of Questions	Assertion Reason 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 Assertion Reason

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Table of Contents

Assertion Reason Questions on Introduction to Euclid’s Geometry

Directions:

a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
b. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
c. Assertion (A) is true but Reason (R) is false.
d. Assertion (A) is false but Reason (R) is true.

Questions:

Q. 1. Assertion (A): According to Euclid’s second axiom, when equals are added to equals, then wholes are equal.
Reason (R): Anil and Mukesh have the same weight. If they each gain weight by 3 kg, second Euclid’s axiom will be used to compare their
weights.

Q. 2. Assertion (A): There can be infinite number of lines that can be drawn through a single point.
Reason (R): From a single point, we can draw only two lines.

Q. 3. Assertion (A): According to the Euclid’s first axiom, ‘Things which are equal to the same thing are also equal to one another’.
Reason (R): If AB = MN and MN = PQ, then AB = PQ.

Solutions:

1. (a) Here both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. (c) Here Assertion (A) is true but Reason (R) is false.

3. (a) Here both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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 assertion reason 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.

Assertion reason questions from the above given topic may be asked.

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Frequently Asked Questions (FAQs) on Introduction to Euclid’s Geometry Assertion Reason Questions Class 9

Q1: What are assertion reason questions?

A1: Assertion-reason questions consist of two statements: an assertion (A) and a reason (R). The task is to determine the correctness of both statements and the relationship between them. The options usually include:
(i) Both A and R are true, and R is the correct explanation of A.
(ii) Both A and R are true, but R is not the correct explanation of A.
(iii) A is true, but R is false.
(iv) A is false, but R is true. or A is false, and R is also false.

Q2: Why are assertion reason questions important in Maths?

A2: Students need to evaluate the logical relationship between the assertion and the reason. This practice strengthens their logical reasoning skills, which are essential in mathematics and other areas of study.

Q3: How can practicing assertion reason questions help students?

A3: Practicing assertion-reason questions can help students in several ways:
Improved Conceptual Understanding: It helps students to better understand the concepts by linking assertions with their reasons.
Enhanced Analytical Skills: It enhances analytical skills as students need to critically analyze the statements and their relationships.
Better Exam Preparation: These questions are asked in exams and practicing them can improve your performance.

Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies:
Understand Each Statement Separately: Determine if each statement is true or false independently.
Analyze the Relationship: If both statements are true, check if the reason correctly explains the assertion.

Q5: What are common mistakes to avoid when answering Assertion Reason questions?

A5: Common mistakes include:
Not reading the statements carefully and missing key details.
Assuming the Reason explains the Assertion without checking the logical connection.
Confusing the order or relationship between the statements.
Overthinking and adding information not provided in the question.

Q6: What are Euclid’s Axioms?

A6: 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.

Q7: What is the difference between an axiom and a theorem in Euclid’s Geometry?

A7: 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.

Q8: Who was Euclid?

A8: 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.

Q9: What is Euclid’s Geometry?

A9: 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.

Q10: Are there any online resources or tools available for practicing Introduction to Euclid’s Geometry assertion reason questions?

A10: We provide assertion reason questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient assertion reason questions and prepare for their exams. If you need more assertion reason questions, then you can visit Physics Gurukul website. they are having a large collection of assertion reason questions for all classes.