case study based questions on quadrilaterals

Class 9 Maths Case Study Questions of Chapter 8 Quadrilaterals PDF Download

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Class 9 Maths Case Study Questions Chapter 8  are very important to solve for your exam. Class 9 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 9 Maths Chapter 8 Quadrilaterals

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These case study questions challenge students to apply their knowledge of quadrilaterals in practical scenarios, enhancing their problem-solving abilities. This article provides the Class 9 Maths Case Study Questions of Chapter 8: Quadrilaterals, enabling students to practice and excel in their examinations.

Quadrilaterals Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 8 Quadrilaterals

Case Study/Passage-Based Questions

Case Study 1: Laveena’s class teacher gave students some colorful papers in the shape of quadrilaterals. She asked students to make a parallelogram from it using paper folding. Laveena made the following parallelogram.

How can a parallelogram be formed by using paper folding? (a) Joining the sides of a quadrilateral (b) Joining the mid-points of sides of a quadrilateral (c) Joining the various quadrilaterals (d) None of these

Answer: (b) Joining the mid-points of sides of quadrilateral

Which of the following is true? (a) PQ = BD (b) PQ = 1/2 BD (c) 3PQ = BD (d) PQ = 2BD

Answer: (b) PQ = 1/2 BD

Which of the following is correct combination? (a) 2RS = BD (b) RS = 1/3 BD (c) RS = BD (d) RS = 2BD

Answer: (a) 2RS = BD

Which of the following is correct? (a) SR = 2PQ (b) PQ = SR (c) SR = 3PQ (d) SR = 4PQ

Answer: (b) PQ = SR

Case Study/Passage Based Questions

Case Study 2: Anjali and Meena were trying to prove mid-point theorem. They draw a triangle ABC, where D and E are found to be the midpoints of AB and AC respectively. DE was joined and extended to F such that DE = EF and FC is also joined.

▲ADE and ▲CFE are congruent by which criterion? (a) SSS (b) SAS (c) RHS (d) ASA

Answer: (b) SAS

∠EFC is equal to which angle? (a) ∠DAE (b) ∠EDA (c) ∠AED (d) ∠DBC

Answer: (b)∠EDA

∠ECF is equal to which angle? (a) ∠EAD (b) ∠ADE (c) ∠AED (d) ∠B

Answer: (a) ∠EAD

CF is equal to (a) EC (b) BE (c) BC (d) AD

Answer: (d) AD

CF is parallel to (a) AE (b) CE (c) BD (d) AC

Answer: (c) BD

Case Study 3. A group of students is exploring different types of quadrilaterals. They encountered the following scenario:

Four friends, Aryan, Bhavana, Chetan, and Divya, participated in a geometry project. They constructed a figure with four sides and made the following observations:

• The opposite sides of the figure are parallel.
• The opposite angles of the figure are congruent.
• The figure has two pairs of congruent adjacent sides.
• The sum of the measures of the interior angles of the figure is 360 degrees.

Based on this information, the students were asked to analyze the properties of the quadrilateral they constructed. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The type of quadrilateral formed by their figure is: (a) Parallelogram (b) Rhombus (c) Rectangle (d) Square

Answer: (a) Parallelogram

Q2. The measure of each angle in the figure is: (a) 90 degrees (b) 120 degrees (c) 135 degrees (d) 180 degrees

Answer: (d) 180 degrees

Q3. The figure is an example of a quadrilateral that satisfies the: (a) Opposite sides are equal condition (b) Opposite angles are congruent condition (c) Diagonals bisect each other condition (d) None of the above

Answer: (b) Opposite angles are congruent condition

Q4. The sum of the measures of the exterior angles of the figure is: (a) 90 degrees (b) 180 degrees (c) 270 degrees (d) 360 degrees

Answer: (d) 360 degrees

Q5. The figure has rotational symmetry of: (a) Order 1 (b) Order 2 (c) Order 3 (d) Order 4

Answer: (a) Order 1

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 8 Quadrilaterals with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Quadrilaterals Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Study Questions for Class 9 Maths Chapter 9 Quadrilaterals

• Last modified on: 3 years ago
• Reading Time: 3 Minutes

Case Study Questions

Question 1:

After summervacation, Manit’s class teacher organised a small MCQ quiz, based on the properties of quadrilaterals. During quiz, she asks different questions to students. Some of the questions are listed below.

(i) Which of the following is/are the condition(s) for ABCD to be a quadrilateral? (a) The four points A, B, C and D must be distinct and co-planar. (b) No three of points A, B, C and D are collinear. (c) Line segments i.e., AB, BC, CD, DA intersect at their end points only. (d) All of these

(ii) Which of the following is wrong condition for a quadrilateral said to be a parallelogram? (a) Opposite sides are equal (b) Opposite angles are equal (c) Diagonal can’t bisect each other (d) None of these

(iii) If AX and CY are the bisectors of the angles A and C of a parallelogram ABCD, then

(a) AX || CY (b) AX || CD (c) AX || AB (d) None of these

(iv) ABCD and AEFG are two parallelograms. If ∠C = 63°, then determine ∠G.

(a) 63° (b) 117° (c) 90° (d) 120°

(v) If angles of a quadrilateral are in ratio 3 : 5 : 5 : 7, then find all the angles. (a) 54°, 80°, 80°, 146° (b) 34°, 100°, 100°, 126° (c) 54°, 90°, 90°, 126° (d) None of these

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3 thoughts on “ Case Study Questions for Class 9 Maths Chapter 9 Quadrilaterals ”

Thank you so much 🥰

Aare bhai question ke sath uska solution bhi to do yaar 🤔🤔. By the way questions was help full

Bat to shai he exam me Rahi questions pucha tha

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Case Study on Quadrilaterals Class 9 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Quadrilaterals Class 9 Maths can use this page to download the PDF file. 

The case study questions on Quadrilaterals are based on the CBSE Class 9 Maths Syllabus, and therefore, referring to the Quadrilaterals case study questions enable students to gain the appropriate knowledge and prepare better for the Class 9 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Quadrilaterals Class 9 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Quadrilaterals, therefore, they prepared a set of solutions along with the case study questions on Quadrilaterals.

The case study on Quadrilaterals Class 9 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Quadrilaterals case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Quadrilaterals Case Study Questions on Class 9 Maths?

There are three major reasons why one should solve Quadrilaterals case study questions on Class 9 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 9 Maths students, therefore, it is important to solve Quadrilaterals Case study questions as it will help better prepare for the Class 9 board exam preparation.
• Develop Problem-Solving Skills: Class 9 Maths Quadrilaterals case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 9 students develop their problem-solving skills, which are essential for success in any profession rather than Class 9 board exam preparation.
• Understand Real-Life Applications: Several Quadrilaterals Class 9 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Quadrilaterals as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Quadrilaterals?

Students can choose their own way to answer Case Study on Quadrilaterals Class 9 Maths, however, we believe following these three steps would help a lot in answering Class 9 Maths Quadrilaterals Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Quadrilaterals questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Quadrilaterals Class 9 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 9 Quadrilaterals?

 A few essential things to know to solve Case Study Questions on Class 9 Quadrilaterals are -

• Basic Formulas of Quadrilaterals: One of the most important things to know to solve Case Study Questions on Class 9 Quadrilaterals is to learn about the basic formulas or revise them before solving the case-based questions on Quadrilaterals.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 9 Maths Quadrilaterals case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Quadrilaterals Class 9 Maths?

Use Selfstudys.com to find Case Study on Quadrilaterals Class 9 Maths. For ease, here is a step-wise procedure to download the Quadrilaterals Case Study for Class 9 Maths in PDF for free of cost.

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• Once the website gets loaded, click on the navigation button

• Find CBSE from the given menu

• Click on Case Study

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• Search Maths and then navigate to the Quadrilaterals Class 9 Maths Case Study

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CBSE Case Study Questions for Class 9 Maths Quadrilaterals Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Quadrilaterals  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 9 Maths Quadrilaterals PDF

Checkout our case study questions for other chapters.

• Chapter 6 Lines and Angles Case Study Questions
• Chapter 7 Triangles Case Study Questions
• Chapter 9 Areas of Parallelograms and Triangles Case Study Questions
• Chapter 10 Circles Case Study Questions

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• Circles Class 9 Case Study Questions Maths Chapter 9

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 9 Circles. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Table of Contents

Case Study Questions on Circles

Government of India is working regularly for the growth of handicapped persons. For these three STD booths situated at point P, Q and R are as shown in the figure, which are operated by handicapped persons. These three booths are equidistant from each other as shown in the figure.

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

Q. 1. Which type of ΔPQR in the given figure?

Q. 2. Measure angle ∠QOR.

Q. 3. Find the value of ∠OQR.

Q. 4. Is it true that points P, Q and R lie on the circle?

1. Given $P, Q$ and $R$ are equidistant. It means their distances are equal.

Note: In an equilateral triangle, length of all three sides are equal. So, $\triangle P Q R$ is an equilateral triangle.

2. Since, $\triangle P Q R$ is an equilateral triangle.

$$ \therefore \angle \mathrm{PQR}=\angle \mathrm{PRQ}=\angle \mathrm{QPR}=60^{\circ} $$

The angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.

$$ \therefore \angle Q O R=2 \angle Q P R=2 \times 60^{\circ}=120^{\circ} $$

3. In $\triangle O Q R$,

$$ O Q=O R[\text { Radii of a circle }) $$

$\Rightarrow \angle \mathrm{ORQ}=\angle \mathrm{OQR}$ [Angles opposite to equal sides of a triangle are equal] Using angle sum property of a triangle,

$$ \begin{aligned} & \angle \mathrm{OQR}+\angle \mathrm{ORQ}+\angle \mathrm{QOR}=180^{\circ} \\ & \Rightarrow \angle \mathrm{OQR}+\angle \mathrm{OQR}+120^{\circ}=180^{\circ} \end{aligned} $$

$$ \begin{gathered} \Rightarrow 2 \angle O Q R=60^{\circ} \\ \therefore \angle O Q R=30^{\circ} \end{gathered} $$

4. Yes, it is true that points $P, Q$ and $R$ lie on the circle.

Understanding Circles

Circle: A collection of all points in a plane which are at a constant distance from a fixed point. The fixed point is called the centre of the circle and the constant distance is called the radius.

In figure, O is the centre, OA is the radius and AB is the diameter of the circle.

Chord: A line segment joining any two points on the circle. In figure, AC is the chord.

Diameter: Longest chord of the circle that passes through the centre of the circle.

Circumference: Length of the boundary of a circle.

Arc: Any part of the circumference of a circle.

In figure, PRQ is minor arc represented as PRQ and PSQ is major arc represented as PSQ.

Semi-circle: Parts of a circle that are divided by its diameter.

Segment: The region between a chord and either of its arcs (major or minor). The segment formed with a minor arc is called minor segment and that formed with a major arc is called major segment.

Sector: The region enclosed by an arc and the two radii joining the centre to the end points of the arc.

The sector corresponding to minor arc is called minor sector i.e., AOB and that corresponding to major arc is called major sector. i.e., AOBCA

• Statistics Class 9 Case Study Questions Maths Chapter 12
• Surface Areas and Volumes Class 9 Case Study Questions Maths Chapter 11
• Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
• 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.

• Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
• The perpendicular from the center of a circle to a chord bisects the chord and onversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
• Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
• The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
• Angles in the same segment of a circle are equal.
• If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
• The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

Circles having same centre are called concentric circles.

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

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Frequently Asked Questions (FAQs) on Circles Case Study

Q1: what is the definition of a circle in class 9 maths.

A1: A circle is defined as the collection of all points in a plane that are at a fixed distance (radius) from a fixed point called the center. In Class 9, the concept of a circle is used to study properties related to chords, tangents, arcs, and sectors.

Q2: What is the difference between a chord and a diameter?

A2: A chord is a line segment joining two points on the circumference of a circle, whereas the diameter is a special chord that passes through the center of the circle. The diameter is the longest chord of the circle and is equal to twice the radius.

Q3: What are tangents and how are they important in this chapter?

A3: A tangent to a circle is a line that touches the circle at exactly one point. Tangents are important in this chapter as you learn properties like “a tangent to a circle is perpendicular to the radius at the point of contact.” You also explore problems involving two tangents drawn from an external point.

Q4: What are the main properties of circles discussed in Class 9 Maths?

A4: The main properties include: (i) The radius is perpendicular to the tangent at the point of contact. (ii) Equal chords are equidistant from the center. (iii) The angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any other point on the circumference.

Q5: What are cyclic quadrilaterals, and how are they related to circles?

A5: A cyclic quadrilateral is a four-sided figure where all its vertices lie on the circumference of a circle. The sum of the opposite angles in a cyclic quadrilateral is always 180°. This property is crucial in solving various geometric problems involving circles.

Q6: How can we prove that the angle subtended by a diameter on the circumference is 90 degrees?

A6: This is a key result derived from the properties of circles. Using the theorem “the angle subtended by a chord at the center is twice the angle subtended at any other point on the circumference,” and since a diameter subtends a straight angle (180°) at the center, it subtends a right angle (90°) on the circumference.

Q7: How many tangents can be drawn from a point outside a circle?

A7: From any point outside a circle, exactly two tangents can be drawn. These tangents have equal lengths from the external point to their points of contact on the circle.

Q8: What are the most important theorems in Chapter 9 of Class 9 Maths?

A8: The two key theorems in this chapter are: (i) The perpendicular from the center of a circle to a chord bisects the chord. (ii) The length of tangents drawn from an external point to a circle are equal.

Q9: Are there any online resources or tools available for practicing Circles case study questions?

A9: 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.

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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

Cbse case study questions for class  9 maths.

CBSE Case Study Questions for Class 9 Maths are a type of assessment where students are given a real-world scenario or situation and they need to apply mathematical concepts to solve the problem. These types of questions help students to develop their problem-solving skills and apply their knowledge of mathematics to real-life situations.

Chapter Wise Case Based Questions for Class 9 Maths

The CBSE Class 9 Case Based Questions can be accessed from Chapetrwise Links provided below:

Chapter-wise case-based questions for Class 9 Maths are a set of questions based on specific chapters or topics covered in the maths textbook. These questions are designed to help students apply their understanding of mathematical concepts to real-world situations and events.

Chapter 1: Number System

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Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

• Case Based Questions: Linear Equations - 1
• Case Based Questions: Linear Equations -2

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

• Case Based Questions: Quadrilaterals - 1
• Case Based Questions: Quadrilaterals - 2

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

• Enhance critical thinking:  Case study questions require students to analyze a real-life scenario and think critically to identify the problem and come up with possible solutions. This enhances their critical thinking and problem-solving skills.
• Apply theoretical concepts:  Case study questions allow students to apply theoretical concepts that they have learned in the classroom to real-life situations. This helps them to understand the practical application of the concepts and reinforces their learning.
• Develop decision-making skills:  Case study questions challenge students to make decisions based on the information provided in the scenario. This helps them to develop their decision-making skills and learn how to make informed decisions.
• Improve communication skills:  Case study questions often require students to present their findings and recommendations in written or oral form. This helps them to improve their communication skills and learn how to present their ideas effectively.
• Enhance teamwork skills:  Case study questions can also be done in groups, which helps students to develop teamwork skills and learn how to work collaboratively to solve problems.

In summary, case study questions are important in Class 9 because they enhance critical thinking, apply theoretical concepts, develop decision-making skills, improve communication skills, and enhance teamwork skills. They provide a practical and engaging way for students to learn and apply their knowledge and skills to real-life situations.

Class 9 Maths Curriculum at Glance

The Class 9 Maths curriculum in India covers a wide range of topics and concepts. Here is a brief overview of the Maths curriculum at a glance:

• Number Systems:  Students learn about the real number system, irrational numbers, rational numbers, decimal representation of rational numbers, and their properties.
• Algebra:  The Algebra section includes topics such as polynomials, linear equations in two variables, quadratic equations, and their solutions.
• Coordinate Geometry:  Students learn about the coordinate plane, distance formula, section formula, and slope of a line.
• Geometry:  This section includes topics such as Euclid’s geometry, lines and angles, triangles, and circles.
• Trigonometry: Students learn about trigonometric ratios, trigonometric identities, and their applications.
• Mensuration: This section includes topics such as area, volume, surface area, and their applications.
• Statistics and Probability:  Students learn about measures of central tendency, graphical representation of data, and probability.

The Class 9 Maths curriculum is designed to provide a strong foundation in mathematics and prepare students for higher education in the field. The curriculum is structured to develop critical thinking, problem-solving, and analytical skills, and to promote the application of mathematical concepts in real-life situations. The curriculum is also designed to help students prepare for competitive exams and develop a strong mathematical base for future academic and professional pursuits.

Students can also access Case Based Questions of all subjects of CBSE Class 9

• Case Based Questions for Class 9 Science
• Case Based Questions for Class 9 Social Science
• Case Based Questions for Class 9 English
• Case Based Questions for Class 9 Hindi
• Case Based Questions for Class 9 Sanskrit

Frequently Asked Questions (FAQs) on Case Based Questions for Class 9 Maths

What is case-based questions.

Case-Based Questions (CBQs) are open-ended problem solving tasks that require students to draw upon their knowledge of Maths concepts and processes to solve a novel problem. CBQs are often used as formative or summative assessments, as they can provide insights into how students reason through and apply mathematical principles in real-world problems.

What are case-based questions in Maths?

Case-based questions in Maths are problem-solving tasks that require students to apply their mathematical knowledge and skills to real-world situations or scenarios.

What are some common types of case-based questions in class 9 Maths?

Common types of case-based questions in class 9 Maths include word problems, real-world scenarios, and mathematical modeling tasks.

Top Courses for Class 9

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