case study for quadrilaterals class 9

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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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

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals where quadrilateral is a four-sided polygon with four vertices and four angles. They are further classified into various types, including rectangle , square, parallelogram, rhombus, trapezium , and kite. The most common examples of quadrilaterals in the real world are the rectangular floor tiles, laptop screens, windows, signboards, etc. Although most of the examples mentioned above can be categorized as rectangles, having a deep understanding of all the types of quadrilaterals will enable students to think through their applications. NCERT Solutions Class 9 Maths Chapter 8 is helpful for the students to understand the concept of Quadrilaterals and their basic properties. This chapter efficiently covers all the important formulas, questions, and theorems based on the angle, diagonals, the sum of angles , and length of the sides of types of quadrilaterals.

Learning the properties of quadrilaterals is helpful in finding the missing angles and sides. The concepts covered in the class 9 maths NCERT solutions chapter 8 quadrilaterals are extremely important as they form the basis of understanding many important topics in higher grades. This chapter will also enable students to explore some practical applications of quadrilaterals in detail through various examples and sample questions. To explore more, you can download the pdf files in the links below and also find some of these in the exercises given below.

• NCERT Solutions Class 9 Maths Chapter 8 Ex 8.1
• NCERT Solutions Class 9 Maths Chapter 8 Ex 8.2

NCERT Solutions for Class 9 Maths Chapter 8 PDF

NCERT solutions maths for class 9 chapter 8 are well-researched resources that promote the analytical skills in students. The questions covered in these exercises are competent to deliver a deep understanding of all the key aspects of quadrilaterals. To prepare these exercises, visit the links of the pdf files given below.

☛ Download Class 9 Maths NCERT Solutions Chapter 8 Quadrilaterals

NCERT Class 9 Maths Chapter 8   Download PDF

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

NCERT solutions class 9 maths chapter 8 concentrates on elaborating the properties of different types of quadrilaterals, especially parallelograms that have many useful applications. These solutions are an amazing way of making learning simple and interesting. They come with a well-organized set of questions providing ample practice and opportunity to apply the acquired knowledge. To learn and practice with NCERT Solutions Class 9 Maths Chapter 8 quadrilaterals, try the exercises given below.

Chapter 8 Quadrilaterals Class 9 Maths

• Class 9 Maths Chapter 8 Ex 8.1 - 12 Questions
• Class 9 Maths Chapter 8 Ex 8.2 - 7 Questions

☛ Download Class 9 Maths Chapter 8 NCERT Book

Topics Covered: The main topics covered in class 9 maths NCERT solutions chapter 8 are the introduction of quadrilaterals, angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram , conditions for a quadrilateral to be a parallelogram, and the mid-point theorem.

Total Questions: Class 9 Maths Chapter 8 Quadrilaterals has a total of 19 questions, which can be subcategorized as short answer types, and moderate ones with sub-questions to facilitate the in-depth understanding of this geometric figure.

List of Formulas in NCERT Solutions Class 9 Maths Chapter 8

Students need to follow a fine preparation strategy to excel in a maths exam, like memorizing some important formulas and concepts with time-bound practice. NCERT solutions class 9 maths chapter 8 includes all the main formulas and concepts with suitable examples for students to grasp them comprehensively. Some of the most important formulas and concepts covered in these NCERT solutions for class 9 maths chapter 8 based on the angle sum property, parallelograms, and mid-point theorem are given below:

• The sum of the angles of a quadrilateral is 360 degrees.
• A quadrilateral with equal and parallel pairs of opposite sides is called a parallelogram.
• The area of a Parallelogram is equal to A = b × h.
• A diagonal of a parallelogram divides it into two congruent triangles.
• In a parallelogram, opposite sides are equal and opposite angles are equal.
• The diagonals of a parallelogram bisect each other.
• The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
• The line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

Important Questions for Class 9 Maths NCERT Solutions Chapter 8

Video solutions for class 9 maths ncert chapter 8, faqs on ncert solutions class 9 maths chapter 8, what is the importance of ncert solutions for class 9 maths chapter 8 quadrilaterals.

Cuemath NCERT Solutions Class 9 Maths are tailored to suit the learning potential of every child as per their grades. These solutions provide comprehension of each topic for students to gain a clear understanding of different geometric shapes. Created as per the NCERT maths textbook, these solutions are sufficient to thoroughly practice and revise the complete chapter 8 of the class 9 maths syllabus. The easy-to-understand format of these solutions is ideal for promoting the problem-solving approach required for higher-level maths studies.

What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 8?

The important topics included in NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals are an introduction to quadrilaterals, their types, basic properties, parallelograms, angle sum property, and midpoint theorem . NCERT solutions class 9 Maths Chapter 8 quadrilaterals nicely cover all these topics with important definitions, axioms, postulates , and examples.

Do I Need to Practice all Questions Provided in Class 9 Maths NCERT Solutions Quadrilaterals?

By regular practice of all the theorems, questions, and examples readily available in the NCERT Solutions Class 9 Maths Chapter 8, students can attain the step-wise approach to answer various types of questions asked in exams. It will also help them gain the necessary confidence required to face home exams or any competitive exams.

How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals?

NCERT Class 9 Maths Chapter 8 quadrilaterals has a total of 19 questions in 2 exercises that adequately cover all the concepts of quadrilaterals. The problems in these exercises are compiled as per the CBSE syllabus that offers clear and precise learning of the entire topic for excellent preparation.

What are the Important Formulas in Class 9 Maths NCERT Solutions Chapter 8?

The important formulas and concepts covered in the NCERT Solutions Class 9 Maths Chapter 8 are based on the sum of quadrilaterals’ angles, types, properties, and theorems. These solutions provide a detailed knowledge of all these concepts through an engaging format with sample exercises explained in a well-organized manner. Understanding these concepts will enable students to solve problems based on them efficiently.

Why Should I Practice NCERT Solutions Class 9 Maths quadrilaterals chapter 8?

The CBSE class 9 maths exams are based on NCERT textbooks, and practicing efficiently with NCERT Solutions Class 9 Maths Chapter 8 quadrilaterals assures that none of the topics is left. Practicing NCERT solutions also help students to acquire the math skills that are beneficial for academics as well as for practical life.

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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

Mycbseguide: blessing in disguise.

Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

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Can I have more questions without downloading the app.

I love math

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CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

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CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

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.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) 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.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) 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.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 8 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 8 Quadrilaterals NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 8 Exercise 8.1

NCERT Solutions for Class 9 Maths Chapter 8 Exercise 8.2

NCERT Solutions for Class 9 Maths Chapter 8 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

• The Mid-point Theorem
• Another Condition for a Quadrilateral to be a Parallelogram
• Properties of a Parallelogram
• Angle Sum Property of a Quadrilateral
• Types of Quadrilaterals

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

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• Math Article
• Quadrilaterals Class 9

Quadrilaterals Class 9 Notes - Chapter 8

Cbse class 9 maths quadrilaterals notes:- download pdf here.

Get the complete notes on quadrilaterals class 9 here. A quadrilateral is a shape which has four sides. In this article, we are going to discuss the different types of quadrilaterals such as square, rectangle, parallelogram properties with proofs.

To know more about Parallelogram, visit here .

Parallelogram: Opposite sides of a parallelogram are equal

In Δ A B C   a n d   Δ C D A

A C = A C [Common / transversal]

∠ B C A = ∠ D A C [alternate angles]

∠ B A C = ∠ D C A [alternate angles]

Opposite angles in a parallelogram are equal

In parallelogram A B C D

A B ‖ C D ; and A C is the transversal

Hence, ∠ 1 = ∠ 3 ….(1) (alternate interior angles)

B C ‖ D A ; and A C is the transversal

Hence, ∠ 2 = ∠ 4 ….(2) (alternate interior angles)

Adding (1) and (2)

∠ 1 + ∠ 2 = ∠ 3 + ∠ 4

∠ B A D = ∠ B C D

Similarly, ∠ A D C = ∠ A B C

Properties of diagonal of a parallelogram

Diagonals of a parallelogram bisect each other.

In  Δ A O B   a n d   Δ C O D ,

∠ 3 = ∠ 5 [alternate interior angles]

∠ 1 = ∠ 2   [vertically opposite angles]

A B = C D [opp. Sides of parallelogram]

Δ A O B ≅ Δ C O D [AAS rule]

Hence, proved

Conversely, If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Diagonal of a parallelogram divides it into two congruent triangles.

In Δ A B C and Δ C D A ,

A B = C D [Opposite sides of parallelogram]

B C = A D [Opposite sides of parallelogram]

A C = A C [Common side]

Hence, proved.

For more information on Properties Of Parallelogram, watch the below video

Diagonals of a rhombus bisect each other at right angles

Diagonals of a rhombus bisect each – other at right angles

In Δ A O D   a n d   Δ C O D ,

O A = O C [Diagonals of parallelogram bisect each other]

O D = O D [Common side]

A D = C D [Adjacent sides of a rhombus]

Δ A O D ≅ Δ C O D [SSS rule]

∠ A O D = ∠ D O C [C.P.C.T]

Hence, ∠ A O D = ∠ D O C = 90

Hence proved.

For more information on Properties Of Rhombus, watch the below video

Diagonals of a rectangle bisect each other and are equal

Rectangle ABCD

In Δ A B C   a n d   Δ B A D ,

A B = B A [Common side]

B C = A D [Opposite sides of a rectangle]

∠ A B C = ∠ B A D [Each = 90 0   ∵ ABCD is a Rectangle]

Δ A B C ≅ Δ B A D [SAS rule]

Consider  Δ O A D   a n d   Δ O C B ,

A D = C B   [Opposite sides of a rectangle]

∠ O A D = ∠ O C B   [ ∵ AD||BC and transversal AC intersects them]

∠ O D A = ∠ O B C   [ ∵ AD||BC and transversal BD intersects them]

Δ O A D ≅ Δ O C B [ASA rule]

Similarly we can prove O B = O D

For more information on Properties Of Rectangle, watch the below video

Diagonals of a square bisect each other at right angles and are equal

Square ABCD

B C = A D [Opposite sides of a Square]

∠ A B C = ∠ B A D [Each = 90 0   ∵ ABCD is a Square]

A D = C B   [Opposite sides of a Square]

In Δ O B A   a n d   Δ O D A ,

O B = O D    [ proved above]

B A = D A   [Sides of a Square]

O A = O A   [ Common side]

Δ O B A ≅ Δ O D A ,   [ SSS rule]

But,  ∠ A O B + ∠ A O D = 180 0   [ Linear pair]

∴ ∠ A O B = ∠ A O D = 90 0

Important results related to parallelograms

Parallelogram ABCD

Opposite sides of a parallelogram are parallel and equal .

A B | | C D , A D | | B C , A B = C D , A D = B C

Opposite angles of a parallelogram are equal adjacent angels are supplementary .

∠ A = ∠ C , ∠ B = ∠ D ,

∠ A + ∠ B = 180 0 , ∠ B + ∠ C = 180 0 , ∠ C + ∠ D = 180 0 , ∠ D + ∠ A = 180 0

A diagonal of parallelogram divides it into two congruent triangles .

Δ A B C ≅ Δ C D A [With respect to AC as diagonal]

The diagonals of a parallelogram bisect each other.

A E = C E , B E = D E

∠ 1 = ∠ 5 (alternate interior angles)

∠ 2 = ∠ 6 (alternate interior angles)

∠ 3 = ∠ 7 (alternate interior angles)

∠ 4 = ∠ 8 (alternate interior angles)

∠ 9 = ∠ 11 (vertically opp. angles)

∠ 10 = ∠ 12 (vertically opp. angles)

The Mid-Point Theorem

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of the third side

In Δ A B C ,  E – the midpoint of A B ;  F – the midpoint of A C

Construction : Produce E F to D such that E F = D F .

In Δ A E F and Δ C D F ,

A F = C F   [ F is the midpoint of AC]

E F = D F [ Construction]

∠ E A F = ∠ D C F ….(1)

D C = E A = E B   [ E is the midpoint of AB]

D C ‖ E A ‖ A B [Since, (1), alternate interior angles]

So E B C D is a parallelogram

Therefore, B C = E D and B C ‖ E D

We have, E F = 1 2 B C and E F | | B C

To know more about Mid-Point Theorem, visit here .

Introduction to Quadrilaterals

For more information on quadrilaterals, watch the below videos.

Quadrilaterals

Any four points in a plane, of which three are non-collinear are joined in order results into a four-sided closed figure called ‘quadrilateral’

Quadrilateral

For more information on Elementary Shapes – Quadrilaterals, watch the below video

To know more about Quadrilaterals, visit here .

Angle sum property of a quadrilateral

Angle sum property – Sum of angles in a quadrilateral is 360

In △ A D C ,

∠ 1 + ∠ 2 + ∠ 4 = 180 (Angle sum property of triangle)…………….(1)

In △ A B C ,

∠ 3 + ∠ 5 + ∠ 6 = 180 (Angle sum property of triangle)………………(2)

∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 + ∠ 5 + ∠ 6 = 360

I.e, ∠ A + ∠ B + ∠ C + ∠ D = 360

Hence proved

Types of Quadrilaterals

A trapezium is a quadrilateral with any one pair of opposite sides parallel .

P Q R S is a trapezium in which P Q | | R S

Parallelogram

A parallelogram is a quadrilateral, with both pair of opposite sides parallel and equal . In a parallelogram, diagonals bisect each other.

Parallelogram ABCD in which A B | | C D , B C | | A D   and A B = C D , B C = A D

A rhombus is a parallelogram with all sides equal.  In a rhombus, diagonals bisect each other perpendicularly

Rhombus ABCD

A rhombus A B C D in which A B = B C = C D = A D and   A C ⊥ B D

A rectangle is a parallelogram with all angles as right angles .

A rectangle A B C D in which, ∠ A = ∠ B = ∠ C = ∠ D = 90 0

A square is a special case of a parallelogram with all angles as right angles and all sides equal.

A   square A B C D in which ∠ A = ∠ B = ∠ C = ∠ D = 90 0 and A B = B C = C D = A D

A kite is a quadrilateral with adjacent sides equal .

A kite A B C D in which A B = B C and A D = C D

For more information on Types Of Quadrilaterals, watch the below videos

To know more about Different Types of Quadrilateral, visit here .

Venn diagram for different types of quadrilaterals

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Test: Quadrilaterals- Case Based Type Questions- 1 - Class 9 MCQ

10 questions mcq test - test: quadrilaterals- case based type questions- 1, harish makes a poster in the shape of a parallelogram on the topic save electricity for an inter school competition as shown in the follow figure. q. if ab = (2y – 3) and cd = 5 cm then what is the value of y.

⇒ 2y – 3 = 5

Harish makes a poster in the shape of a parallelogram on the topic SAVE ELECTRICITY for an inter school competition as shown in the follow figure. Q. If ∠B = (2y)° and ∠D = (3y – 6)°, then find the value of y.

(opposite angles of a parallelogram are equal)

⇒ 2y = 3y – 6

⇒ 2y – 3y = – 6

⇒ – y = – 6

Harish makes a poster in the shape of a parallelogram on the topic SAVE ELECTRICITY for an inter school competition as shown in the follow figure. Q. If ∠ A = (4x + 3)° and ∠D = (5x – 3)°, then find the measure of ∠B

∠A + ∠D = 180°

(adjacent angles of a quadrilateral are equal)

(4x + 3)° + (5x – 3)° = 180°

∠D = (5x – 3)° = 97°

Thus, ∠B = 97°

Harish makes a poster in the shape of a parallelogram on the topic SAVE ELECTRICITY for an inter school competition as shown in the follow figure.

Q. If ∠A = (2x – 3)° and ∠C = (4y + 2)°, then find how x and y relate.

• A. x = 2y + 3

• D. x = y – 7

⇒ 2x – 3 = 4y + 2

⇒ 2x = 4y + 5

Q. Which mathematical concept is used here?

• A. Co-ordinate geometry
• B. Surface area and volume
• C. Properties of a parallelogram
• D. Probability

If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.

During maths lab activity, teacher gives four sticks of lengths 6 cm, 6 cm, 4 cm and 4 cm to each student to make different types of quadrilateral.

She asks following questions from the students:

Q. A student formed a rectangle with these sticks. What is the length of the diagonal of the rectangle formed by the student?

6 2 + 4 2 = l 2

36 + 16 = l 2

Q. Write the name of quadrilateral that can be formed with these sticks.

• A. Kite, rectangle, rhombus
• B. Parallelogram, rectangle , trapezium
• C. Kite, rectangle, parallelogram
• D. Square, rectangle, kite

Q. How many types of quadrilaterals can be possible?

Q. Which statement is incorrect ?

• A. Opposite sides of a parallelogram are equal
• B. A kite is not a parallelogram
• C. Diagonals of a parallelogram bisect each other
• D. A trapezium is a parallelogram.

Q. A diagonal of a parallelogram divides it into two _______ triangles.

• B. Congruent
• C. Equilateral
• D. Right angled

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Important Questions for Quadrilaterals- Case Based Type Questions- 1

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Unit 12: Quadrilaterals

Angles of a polygon.

• Sum of interior angles of a polygon (Opens a modal)
• Sum of the exterior angles of a polygon (Opens a modal)
• Angles of a polygon Get 3 of 4 questions to level up!
• Interior and exterior angles of a polygon Get 3 of 4 questions to level up!

Types of quadrilaterals part 1

• Intro to quadrilateral (Opens a modal)
• Quadrilateral properties (Opens a modal)
• Quadrilateral types (Opens a modal)
• Identify quadrilaterals Get 5 of 7 questions to level up!

Types of quadrilaterals part 2

• Classifying quadrilaterals (Opens a modal)
• Kites as a geometric shape (Opens a modal)
• Analyze quadrilaterals Get 3 of 4 questions to level up!
• Quadrilateral types Get 3 of 4 questions to level up!

Properties of parallelograms part 1

• Proof: Opposite sides of a parallelogram (Opens a modal)
• Proof: Diagonals of a parallelogram (Opens a modal)
• Proof: Opposite angles of a parallelogram (Opens a modal)
• Side and angle properties of a parallelogram (level 1) Get 3 of 4 questions to level up!

Properties of parallelograms part 2

• Proof: Rhombus diagonals are perpendicular bisectors (Opens a modal)
• Rhombus diagonals (Opens a modal)
• Diagonal properties of parallelogram Get 3 of 4 questions to level up!
• Side and angle properties of a parallelogram (level 2) Get 3 of 4 questions to level up!

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

Ncert solutions for class 9 maths chapter 8 quadrilaterals| pdf download.

• Exercise 8.1 Chapter 8 Class 9 Maths NCERT Solutions
• Exercise 8.2 Chapter 8 Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapters:

What are the benefits of ncert solutions for chapter 8 quadrilaterals class 9 ncert solutions, what is a rhombus, what is mid-point theorem, in a quadrilateral, ∠ a : ∠ b : ∠ c : ∠ d = 1 : 2 : 3 : 4, then find the measure of each angle of the quadrilateral., contact form.