case study questions from 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

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Case Study Questions for Class 9 Maths Chapter 9 Quadrilaterals

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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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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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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.

Table of Contents

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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Test: Quadrilaterals- Case Based Type Questions- 2 - Class 9 MCQ

10 questions mcq test - test: quadrilaterals- case based type questions- 2, abcd is an area in the shape of rhombus in which ∠adc = 120°. samay and tarun lived at d and c and their school located at o. q. who can reach school early.

• C. Both will reach at same time
• D. Cannot say

Since, ∠CDO > ∠ DCO

(side opposite to greater angle is greater.)

⇒ Samay will reach school early.

ABCD is an area in the shape of rhombus in which ∠ADC = 120°. Samay and Tarun lived at D and C and their school located at O. Q. Measure of ∠CDO and ∠DCO are ______ and ______ respectively.

120°, 50°

30°, 60°

60°, 30°

120°, 60°

Diagonal of a rhombus bisects the angles is passing from.

∠CDO = 1/2 ∠CDA

= 1/2 (120)° = 60°

∠ADC + ∠DCB = 180°

120° + ∠DCB = 180°

⇒ ∠DCB = 180° – 120° = 60°

∠DCO = 1/2 ∠DCB

= 1/2 (60°) = 30°

ABCD is an area in the shape of rhombus in which ∠ADC = 120°. Samay and Tarun lived at D and C and their school located at O. Q. Measure of ∠DCB is :

Thus, ∠CDA + ∠DCB = 180°

⇒ 120° + ∠DCB = 180°

⇒ ∠DCB = 180° – 120° = 60°

ABCD is an area in the shape of rhombus in which ∠ADC = 120°. Samay and Tarun lived at D and C and their school located at O.

Q. Which statement is incorrect?

• A. A rhombus has all the properties of a parallelogram.
• B. Diagonals of the rhombus are angle bisectors.
• C. Sum of consecutive angles of a rhombus is 180°.
• D. Diagonals of a rhombus are not perpendicular bisectors.

Diagonals of a rhombus are perpendicular bisectors.

Q. Measure of ∠BAC :

Thus, ∠BAC = ∠ DCA = 30° (alternate interior angles)

Maths teacher of class 9th gave students coloured paper in the shape of quadrilateral and then ask the students to make parallelogram from it by using paper folding.

Q. If S P = 3 cm, then RQ =

Q. If ∠RSP = 30°, then ∠RQP =

Q. How can a parallelogram be formed by using paper folding?

• A. By joining any two vertices
• B. By joining one pair of opposite vertices.
• C. By joining mid points of sides of a quadrilateral
• D. None of the above

Q. If ∠RSP = 50°, then ∠SPQ =

Thus, ∠RSP + ∠SPQ = 180°

50° + ∠SPQ = 180°

∠SPQ = 180° – 50°

Q. Which statement is incorrect about the parallelogram?

• A. Consecutive angles are supplementary
• B. Opposites sides are parallel
• C. Diagonal bisects each other
• D. Diagonals are equal in length.

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CBSE Class 9 Mathematics Case Study Questions

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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)

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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.

Where is search ? bar

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Can I have more questions without downloading the app.

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Unit 11: Quadrilaterals

• Polygons as special curves (Opens a modal)
• Open and closed curves Get 3 of 4 questions to level up!
• Polygon types Get 3 of 4 questions to level up!

Angle sum property

• 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!

Kinds of quadrilaterals

• Intro to quadrilateral (Opens a modal)
• Quadrilateral types (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 a parallelogram

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

• Class 9 Maths MCQs
• Chapter 8 Quadrilaterals Mcq

Class 9 Maths Chapter 8 Quadrilaterals MCQs

Class 9 Maths Chapter 8 Quadrilaterals MCQs are available here with answers, online. The questions are prepared, as per the CBSE syllabus and NCERT curriculum. Students can prepare for exams with the help of these objective questions to score good marks. The answers are available with detailed explanations. Get chapter-wise MCQs at BYJU’S and also check Important Questions for Class 9 Maths .

To get more MCQs on Class 9 Maths Chapter 8, click on the below link.

Class 9 Maths Chapter 8 Quadrilaterals MCQs – Practice Questions

MCQs on Class 9 Maths Chapter 8 Quadrilaterals

Solve the questions provided below with four multiple options and choose the correct one.

1) The quadrilateral whose all its sides are equal and angles are equal to 90 degrees, it is called:

a. Rectangle

d. Parallelogram

2) The sum of all the angles of a quadrilateral is equal to:

3) A trapezium has:

a. One pair of opposite sides parallel

b. Two pairs of opposite sides parallel to each other

c. All its sides are equal

d. All angles are equal

Explanation: A trapezium has only one pair of opposite sides parallel to each other, and the other two sides are non-parallel.

4) A rhombus can be a:

a. Parallelogram

b. Trapezium

5) A diagonal of a parallelogram divides it into two congruent:

b. Parallelogram

c. Triangles

d. Rectangle

6) In a parallelogram, opposite angles are:

c. Cannot be determined

d. None of the above

7) The diagonals of a parallelogram:

c. Bisect each other

d. Have no relation

8) Each angle of the rectangle is:

a. More than 90°

b. Less than 90°

c. Equal to 90°

d. Equal to 45°

Explanation: Let ABCD is a rectangle, and ∠A = 90°

AD || BC and AB is a transversal

∠ A + ∠ B = 180° (Interior angles on the same side of the transversal)

So, ∠ B = 180° – ∠ A = 180° – 90° = 90°

Now, ∠ C = ∠ A and ∠ D = ∠ B (Opposite angles of the parallelogram)

So, ∠ C = 90° and ∠ D = 90°

Hence all sides are equals to 90°.

9) The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The angles are:

a. 36°, 60°, 108°, 156°

b. 48°, 60°, 120°, 132°

c. 52°, 60°, 122°, 126°

d. 60°, 60°, 120°, 120°

Explanation: Let x be the common angle among all the four angles of a quadrilateral.

As per angle sum property, we know:

4x+5x+10x+11x = 360°

Hence, angles are

4x = 4 (12) = 48°

5x = 5 (12) = 60°

10x = 10 (12) = 120°

11x = 11 (12) = 132°

10) If ABCD is a trapezium in which AB || CD and AD = BC, then:

b. ∠A > ∠B

c. ∠A < ∠B

Explanation: Draw a line through C parallel to DA intersecting AB produced at E.

CE = AD (Opposite sides)

AD = BC (Given)

⇒ ∠CBE = ∠CEB

∠A + ∠CBE = 180° (Angles on the same side of transversal and ∠CBE = ∠CEB)

∠B + ∠CBE = 180° ( As Linear pair)

11) Which of the following is not true for a parallelogram?

(a) Opposite sides are equal

(b) Opposite angles are equal

(c) Opposite angles are bisected by the diagonals

(d) Diagonals bisect each other.

Explanation: Opposite angles are bisected by the diagonals is not true for a parallelogram. Whereas opposite sides are equal, opposite angles are equals, diagonals bisect each other are the properties of a parallelogram.

12) Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is

Explanation: We know that the sum of angles of a quadrilateral is 360º.

Let the unknown angle be x.

Therefore, 75º+90º+75º+x = 360º

x = 360º – 240º = 120º.

13) ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is

Explanation: We know that the diagonals of the rhombus bisect each other perpendicularly.

By using the alternate interior angles, and angle sum property of triangle, we can say:

From the triangle, BOC,

∠BOC + ∠OCB + ∠OBC = 180º

(where  ∠BOC= 90º, ∠OCB = 40º)

90º+40º+ ∠OBC = 180º

∠OBC = 180º – 130º

Now, by using alternate angles, we can say

14) The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if

(a) PQRS is a rhombus

(b) PQRS is a parallelogram

(c) Diagonals of PQRS are perpendicular

(d) Diagonals of PQRS are equal.

Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus if the diagonals of PQRS are equal.

15) A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is

Explanation: Consider the rectangle ABCD

In a triangle BOC, 

∠OBC = ∠OCB (Opposite angles of isosceles triangle)

Therefore, ∠OBC + ∠OCB+∠BOC = 180º

25º+25º + ∠BOC = 180º

∠BOC = 180º- 50º

∠BOC = 130º.

By using the linear pair, 

∠AOB + ∠BOC = 180º

∠AOB = 180º – 130º

Hence, the acute angle between the diagonals is 50º.

16) If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a

(b) Rhombus

(c) Parallelogram

(d) Trapezium

Explanation: 

Given that, the angles A, B, C and D of a quadrilateral are in the ratio 3:7:6:4.

We know that A+B+C+D = 360º

Hence, now we can assume, 3k+7k+6k+4k= 360º

Therefore, A = 3k = 54º

B= 7k = 126º

C = 6k = 108º

D = 4k= 72º

If we draw the quadrilateral with these angles, we get a trapezium.

17) The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

(a) PQRS is a rectangle

(d) Diagonals of PQRS are equal

Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if the diagonals of PQRS are perpendicular.

18) The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is

(a) a square

(b) a rhombus

(c) a rectangle

(d) any parallelogram

Explanation: Let ABCD be a rhombus. P, Q, R, S be the midpoint of the sides AB, BC, CD and DA. If we join the midpoints, we will get the shape rectangle.

19) If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form

(b) Rectangle

(c) Rhombus

(d) any other parallelogram

Explanation:

Hence, the bisectors of the angles APQ, BPQ, CQP and PQD form the shape rectangle.

20) Which of the following is not a quadrilateral?

(c) Triangle

(d) Rhombus

Explanation: square, kite and rhombus are quadrilaterals as it has four sides. Whereas a triangle is not a quadrilateral as it has only three sides.

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