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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.
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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.
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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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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download
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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
- Case Based Questions: Number System
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
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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.
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FAQs on CBSE Case Study Questions for Class 9 Maths - Pdf
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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)
I | NUMBER SYSTEMS | 10 |
II | ALGEBRA | 20 |
III | COORDINATE GEOMETRY | 04 |
IV | GEOMETRY | 27 |
V | MENSURATION | 13 |
VI | STATISTICS & PROBABILITY | 06 |
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)
1. | Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas | 43 | 54 |
2. | Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. | 19 | 24 |
3. | Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions | 18 | 22 |
80 | 100 |
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.
Where is search ? bar
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Can I have more questions without downloading the app.
I love math
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CBSE Class 9 Maths Most Important Case Study Based Questions With Solution
Cbse class 9 mathematics case study questions.
In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are preparing for their final class 9 maths exam.
![case study class 9 maths chapter 7 CBSE Class 9 Mathematics Case Study Questions](https://mrmanojpandey.com/wp-content/uploads/2023/03/CBSE-class-9-maths-1024x576.jpg)
All these questions provided in this article are with solution which will help students for solving the problems. Dear students need to practice all these questions carefully with the help of given solutions.
As you know CBSE Class 9 Maths exam will have a set of cased study based questions in the form of MCQs. CBSE Class 9 Maths Question Bank given in this article can be very helpful in understanding the new format of questions for new session.
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Case studies in class 9 mathematics.
The Central Board of Secondary Education (CBSE) has included case study based questions in the Class 9 Mathematics paper in current session. According to new pattern CBSE Class 9 Mathematics students will have to solve case based questions. This is a departure from the usual theoretical conceptual questions that are asked in Class 9 Maths exam in this year.
Each question provided in this post has five sub-questions, each followed by four options and one correct answer. All CBSE Class 9th Maths Students can easily download these questions in PDF form with the help of given download Links and refer for exam preparation.
There is many more free study materials are available at Maths And Physics With Pandey Sir website. For many more books and free study material all of you can visit at this website.
Given Below Are CBSE Class 9th Maths Case Based Questions With Their Respective Download Links.
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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023
By QB365 on 08 Sep, 2022
QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
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Coordinate geometry case study questions with answer key.
9th Standard CBSE
Final Semester - June 2015
Mathematics
(b) What are the coordinates of C and D respectively?
(c) What is the distance between B and D?
(d) What is the distance between A and C?
(e) What are the coordinates of the point of intersection of AC and BD?
(ii) What are the coordinates of Police Station?
(iii) Distance between school and police station:
(iv) What are the coordinates of Library?
(v) In which quadrant the point (-1, 4) lies?
(b) What are the coordinates of A and B respectively?
(c) The coordinates of point O in the sketch -2 is
(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is
(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is
(b) What are the coordinates of R, taking A as origin?
(c) Side of lawn is :
units |
(d) Shape of lawn is :
(e) Area of lawn is :
(ii) What are the coordinates of position 'D'?
(iii) What are the coordinates of position 'H'?
(iv) In which quadrant, the point 'C' lie?
(v) Find the perpendicular distance of the point E from the y-axis.
*****************************************
Coordinate geometry case study questions with answer key answer keys.
(a) (iii) A(3, 5); B(7, 9) (b) (i) C(11, 5); D(7, 1) (c) (iii) 8 units (d) (iii) 8 units (e) (i) (7, 5)
(i) (b) (2, 3) (ii) (a) (2, -1) (iii) (a) 4 (iv) (d) (6, 2) (v) (b) II
(a) (ii) A(13, 10); B(19, 10) (b) (iv) A(19, 6); B(13, 6) (c) (ii) (16, 8) (d) (i) (0, 8) (e) (ii) (16, 0)
(a) (iv) C(10, 6) (b) (iii) R(5, 6) (c) (ii) \(\sqrt{34}\) units PS 2 = AS 2 + AP 2 = 5 2 + 3 2 = 25 + 9 = 34 ⇒ PS = \(\sqrt{34}\) (d) (iv) Rhombus (e) (i) 30 sq. units Area of rhombus = \(1 / 2\) x product of diagonals = \(1 / 2\) x 6 x 10 = 30 sq. units
(i) (d) (-4, 3) (ii) (b) (-3, -2) (iii) (b) (8, 4.5) (iv) (d) IV (v) (b) 10 units
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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.
Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.
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NCERT Solutions for Class 9 Maths Chapter 7 Triangles
NCERT Solutions for Class 9 Maths Chapter 7 Triangles 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 7 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 7 Triangles 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 7 Exercise 7.1
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NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.2
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NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.3
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NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4
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NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.5
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NCERT Solutions for Class 9 Maths Chapter 7 – Topic Discussion
Below we have listed the topics that have been discussed in this chapter.
- Congruence of triangles.
- Criteria for congruence of triangles (SAS congruence rule, ASA congruence rule, SSS congruence rule, RHS congruence rule).
- Properties of triangles.
- Inequalities of triangle.
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- NCERT Solutions
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NCERT Solutions for Class 9 Maths Chapter 7 - Triangles
Ncert solutions for class 9 maths chapter 7 – cbse free pdf download.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles provides the answers and questions related to the chapter as included in the CBSE Syllabus for 2023-24. The word triangle itself describes its meaning. “Tri” means “three”,; so a closed figure formed by three intersecting lines is known as a Triangle. Students must have already studied the angle sum property of a triangle in Chapter 6 of NCERT Class 9 Maths. Now, in continuation to it, Chapter 7 of NCERT Solutions for Class 9 Maths will brief students about the congruence of triangles and the rules of congruence. Also, they will learn a few more properties of triangles and inequalities in a triangle.
Download Exclusively Curated Chapter Notes for Class 9 Maths Chapter – 7 Goemetry of Triangles
Download most important questions for class 9 maths chapter – 7 goemetry of triangles.
Here we have provided the complete Class 9 Maths NCERT Solutions Chapter 7 Triangles in PDF format solved by experienced teachers. Students can download the free PDF of these NCERT Solutions for Class 9 by clicking on the link below to keep it handy for future reference.
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NCERT Solutions for Class 9 Maths Chapter 7 – Triangles
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List of Exercises in NCERT Class 9 Maths Chapter 7
Exercise 7.1 Solution 8 Questions (6 Short Answer Questions, 2 Long Answer Question) Exercise 7.2 Solution 8 Questions (6 Short Answer Questions, 2 Long Answer Question) Exercise 7.3 Solution 5 Questions (3 Short Answer Questions, 2 Long Answer Question) Exercise 7.4 Solution 6 Questions (5 Short Answer Questions, 1 Long Answer Question) Exercise 7.5 (Optional) Solution 4 Questions
Access Answers of Maths NCERT Class 9 Chapter 7 – Triangles
Exercise: 7.1 (Page No: 118)
1. In quadrilateral ACBD, AC = AD and AB bisect ∠A (see Fig. 7.16). Show that ΔABC≅ ΔABD. What can you say about BC and BD?
![Ncert solutions class 9 chapter 7-1 Ncert solutions class 9 chapter 7-1](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-1.jpeg)
It is given that AC and AD are equal i.e. AC = AD and the line segment AB bisects ∠A.
We will have to now prove that the two triangles ABC and ABD are similar i.e. ΔABC ≅ ΔABD
Consider the triangles ΔABC and ΔABD,
(i) AC = AD (It is given in the question)
(ii) AB = AB (Common)
(iii) ∠CAB = ∠DAB (Since AB is the bisector of angle A)
So, by SAS congruency criterion , ΔABC ≅ ΔABD.
For the 2 nd part of the question, BC and BD are of equal lengths by the rule of C.P.C.T.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-1.jpg)
2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that
(i) ΔABD ≅ ΔBAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.
![Ncert solutions class 9 chapter 7-2 Ncert solutions class 9 chapter 7-2](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-2.png)
The given parameters from the questions are ∠ DAB = ∠ CBA and AD = BC.
(i) ΔABD and ΔBAC are similar by SAS congruency as
AB = BA (It is the common arm)
∠ DAB = ∠ CBA and AD = BC (These are given in the question)
So, triangles ABD and BAC are similar i.e. ΔABD ≅ ΔBAC. (Hence proved).
(ii) It is now known that ΔABD ≅ ΔBAC so,
BD = AC (by the rule of CPCT).
(iii) Since ΔABD ≅ ΔBAC so,
Angles ∠ ABD = ∠ BAC (by the rule of CPCT).
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-2.jpg)
3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.
![Ncert solutions class 9 chapter 7-3 Ncert solutions class 9 chapter 7-3](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-3.png)
It is given that AD and BC are two equal perpendiculars to AB.
We will have to prove that CD is the bisector of AB
Triangles ΔAOD and ΔBOC are similar by AAS congruency since:
(i) ∠A = ∠B (They are perpendiculars)
(ii) AD = BC (As given in the question)
(iii) ∠AOD = ∠BOC (They are vertically opposite angles)
∴ ΔAOD ≅ ΔBOC.
So, AO = OB (by the rule of CPCT).
Thus, CD bisects AB (Hence proved).
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-3.jpg)
4. l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ΔABC ≅ ΔCDA.
![Ncert solutions class 9 chapter 7-4 Ncert solutions class 9 chapter 7-4](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-4.jpeg)
It is given that p || q and l || m
Triangles ABC and CDA are similar i.e. ΔABC ≅ ΔCDA
Consider the ΔABC and ΔCDA,
(i) ∠BCA = ∠DAC and ∠BAC = ∠DCA Since they are alternate interior angles
(ii) AC = CA as it is the common arm
So, by ASA congruency criterion, ΔABC ≅ ΔCDA.
5. Line l is the bisector of an angle ∠A and B is any point on l . BP and BQ are perpendiculars from B to the arms of ∠A (see Fig. 7.20). Show that:
(i) ΔAPB ≅ ΔAQB
(ii) BP = BQ or B is equidistant from the arms of ∠A.
![Ncert solutions class 9 chapter 7-5 Ncert solutions class 9 chapter 7-5](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-5.jpeg)
It is given that the line “ l ” is the bisector of angle ∠A and the line segments BP and BQ are perpendiculars drawn from l .
(i) ΔAPB and ΔAQB are similar by AAS congruency because:
∠P = ∠Q (They are the two right angles)
AB = AB (It is the common arm)
∠BAP = ∠BAQ (As line l is the bisector of angle A)
So, ΔAPB ≅ ΔAQB.
(ii) By the rule of CPCT, BP = BQ. So, it can be said the point B is equidistant from the arms of ∠A.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-5.jpg)
6. In Fig. 7.21, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-6](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-6.png)
It is given in the question that AB = AD, AC = AE, and ∠BAD = ∠EAC
The line segment BC and DE are similar i.e. BC = DE
We know that ∠BAD = ∠EAC
Now, by adding ∠DAC on both sides we get,
∠BAD + ∠DAC = ∠EAC +∠DAC
This implies, ∠BAC = ∠EAD
Now, ΔABC and ΔADE are similar by SAS congruency since:
(i) AC = AE (As given in the question)
(ii) ∠BAC = ∠EAD
(iii) AB = AD (It is also given in the question)
∴ Triangles ABC and ADE are similar i.e. ΔABC ≅ ΔADE.
So, by the rule of CPCT, it can be said that BC = DE.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-6.jpg)
7. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (see Fig. 7.22). Show that
(i) ΔDAP ≅ ΔEBP
(ii) AD = BE
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-7](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-7.png)
In the question, it is given that P is the mid-point of line segment AB. Also, ∠BAD = ∠ABE and ∠EPA = ∠DPB
(i) It is given that ∠EPA = ∠DPB
Now, add ∠DPE on both sides,
∠EPA +∠DPE = ∠DPB+∠DPE
This implies that angles DPA and EPB are equal i.e. ∠DPA = ∠EPB
Now, consider the triangles DAP and EBP.
∠DPA = ∠EPB
AP = BP (Since P is the mid-point of the line segment AB)
∠BAD = ∠ABE (As given in the question)
So, by ASA congruency , ΔDAP ≅ ΔEBP.
(ii) By the rule of CPCT, AD = BE.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.1-Question-Number-7.jpg)
8. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig. 7.23). Show that:
(i) ΔAMC ≅ ΔBMD
(ii) ∠DBC is a right angle.
(iii) ΔDBC ≅ ΔACB
(iv) CM = ½ AB
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-8](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-8.png)
It is given that M is the mid-point of the line segment AB, ∠C = 90°, and DM = CM
(i) Consider the triangles ΔAMC and ΔBMD:
AM = BM (Since M is the mid-point)
CM = DM (Given in the question)
∠CMA = ∠DMB (They are vertically opposite angles)
So, by SAS congruency criterion , ΔAMC ≅ ΔBMD.
(ii) ∠ACM = ∠BDM (by CPCT)
∴ AC || BD as alternate interior angles are equal.
Now, ∠ACB +∠DBC = 180° (Since they are co-interiors angles)
⇒ 90° +∠B = 180°
∴ ∠DBC = 90°
(iii) In ΔDBC and ΔACB,
BC = CB (Common side)
∠ACB = ∠DBC (They are right angles)
DB = AC (by CPCT)
So, ΔDBC ≅ ΔACB by SAS congruency .
(iv) DC = AB (Since ΔDBC ≅ ΔACB)
⇒ DM = CM = AM = BM (Since M the is mid-point)
So, DM + CM = BM+AM
Hence, CM + CM = AB
⇒ CM = (½) AB
Exercise: 7.2 (Page No: 123)
1. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
(i) OB = OC (ii) AO bisects ∠A
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-9](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-9.png)
AB = AC and
the bisectors of ∠B and ∠C intersect each other at O
(i) Since ABC is an isosceles with AB = AC,
½ ∠B = ½ ∠C
⇒ ∠OBC = ∠OCB (Angle bisectors)
∴ OB = OC (Side opposite to the equal angles are equal.)
(ii) In ΔAOB and ΔAOC,
AB = AC (Given in the question)
AO = AO (Common arm)
OB = OC (As Proved Already)
So, ΔAOB ≅ ΔAOC by SSS congruence condition.
BAO = CAO (by CPCT)
Thus, AO bisects ∠A.
2. In ΔABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ΔABC is an isosceles triangle in which AB = AC.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-10](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-10.png)
It is given that AD is the perpendicular bisector of BC
In ΔADB and ΔADC,
AD = AD (It is the Common arm)
∠ADB = ∠ADC
BD = CD (Since AD is the perpendicular bisector)
So, ΔADB ≅ ΔADC by SAS congruency criterion .
AB = AC (by CPCT)
3. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-11](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-11.png)
(i) BE and CF are altitudes.
(ii) AC = AB
Triangles ΔAEB and ΔAFC are similar by AAS congruency since
∠A = ∠A (It is the common arm)
∠AEB = ∠AFC (They are right angles)
∴ ΔAEB ≅ ΔAFC and so, BE = CF (by CPCT).
4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that
(i) ΔABE ≅ ΔACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-12](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-12.png)
It is given that BE = CF
(i) In ΔABE and ΔACF,
∠A = ∠A (It is the common angle)
BE = CF (Given in the question)
∴ ΔABE ≅ ΔACF by AAS congruency condition .
(ii) AB = AC by CPCT and so, ABC is an isosceles triangle.
5. ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-13](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-13.png)
In the question, it is given that ABC and DBC are two isosceles triangles.
We will have to show that ∠ABD = ∠ACD
Triangles ΔABD and ΔACD are similar by SSS congruency since
AD = AD (It is the common arm)
AB = AC (Since ABC is an isosceles triangle)
BD = CD (Since BCD is an isosceles triangle)
So, ΔABD ≅ ΔACD.
∴ ∠ABD = ∠ACD by CPCT.
6. ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠BCD is a right angle.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-14](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-14.jpeg)
It is given that AB = AC and AD = AB
We will have to now prove ∠BCD is a right angle.
Consider ΔABC,
AB = AC (It is given in the question)
Also, ∠ACB = ∠ABC (They are angles opposite to the equal sides and so, they are equal)
Now, consider ΔACD,
Also, ∠ADC = ∠ACD (They are angles opposite to the equal sides and so, they are equal)
∠CAB + ∠ACB + ∠ABC = 180°
So, ∠CAB + 2∠ACB = 180°
⇒ ∠CAB = 180° – 2∠ACB — (i)
Similarly, in ΔADC,
∠CAD = 180° – 2∠ACD — (ii)
∠CAB + ∠CAD = 180° (BD is a straight line.)
Adding (i) and (ii) we get,
∠CAB + ∠CAD = 180° – 2∠ACB+180° – 2∠ACD
⇒ 180° = 360° – 2∠ACB-2∠ACD
⇒ 2(∠ACB+∠ACD) = 180°
⇒ ∠BCD = 90°
7. ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
![Ncert solutions class 9 chapter 7 Ncert solutions class 9 chapter 7-15](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-15.jpeg)
In the question, it is given that
∠A = 90° and AB = AC
⇒ ∠B = ∠C (They are angles opposite to the equal sides and so, they are equal)
∠A+∠B+∠C = 180° (Since the sum of the interior angles of the triangle)
∴ 90° + 2∠B = 180°
⇒ 2∠B = 90°
So, ∠B = ∠C = 45°
8. Show that the angles of an equilateral triangle are 60° each.
Let ABC be an equilateral triangle as shown below:
![Ncert solutions class 9 chapter 7-16 Ncert solutions class 9 chapter 7-16](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-16.png)
Here, BC = AC = AB (Since the length of all sides is same)
⇒ ∠A = ∠B =∠C (Sides opposite to the equal angles are equal.)
Also, we know that
∠A+∠B+∠C = 180°
⇒ 3∠A = 180°
∴ ∠A = ∠B = ∠C = 60°
So, the angles of an equilateral triangle are always 60° each.
Exercise: 7.3 (Page No: 128)
1. ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that
(i) ΔABD ≅ ΔACD
(ii) ΔABP ≅ ΔACP
(iii) AP bisects ∠A as well as ∠D.
(iv) AP is the perpendicular bisector of BC.
![Ncert solutions class 9 chapter 7-17 Ncert solutions class 9 chapter 7-17](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-17.png)
In the above question, it is given that ΔABC and ΔDBC are two isosceles triangles.
(i) ΔABD and ΔACD are similar by SSS congruency because:
AB = AC (Since ΔABC is isosceles)
BD = CD (Since ΔDBC is isosceles)
∴ ΔABD ≅ ΔACD.
(ii) ΔABP and ΔACP are similar as:
AP = AP (It is the common side)
∠PAB = ∠PAC (by CPCT since ΔABD ≅ ΔACD)
So, ΔABP ≅ ΔACP by SAS congruency condition.
(iii) ∠PAB = ∠PAC by CPCT as ΔABD ≅ ΔACD.
AP bisects ∠A. — (i)
Also, ΔBPD and ΔCPD are similar by SSS congruency as
PD = PD (It is the common side)
BD = CD (Since ΔDBC is isosceles.)
BP = CP (by CPCT as ΔABP ≅ ΔACP)
So, ΔBPD ≅ ΔCPD.
Thus, ∠BDP = ∠CDP by CPCT. — (ii)
Now by comparing (i) and (ii) it can be said that AP bisects ∠A as well as ∠D.
(iv) ∠BPD = ∠CPD (by CPCT as ΔBPD ΔCPD)
and BP = CP — (i)
∠BPD +∠CPD = 180° (Since BC is a straight line.)
⇒ 2∠BPD = 180°
⇒ ∠BPD = 90° —(ii)
Now, from equations (i) and (ii), it can be said that
AP is the perpendicular bisector of BC.
2. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC (ii) AD bisects ∠A.
It is given that AD is an altitude and AB = AC. The diagram is as follows:
![Ncert solutions class 9 chapter 7-18 Ncert solutions class 9 chapter 7-18](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-18.png)
(i) In ΔABD and ΔACD,
∠ADB = ∠ADC = 90°
AD = AD (Common arm)
∴ ΔABD ≅ ΔACD by RHS congruence condition.
Now, by the rule of CPCT,
So, AD bisects BC
(ii) Again, by the rule of CPCT, ∠BAD = ∠CAD
Hence, AD bisects ∠A.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.3-Question-Number-2.jpg)
3. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see Fig. 7.40). Show that:
(i) ΔABM ≅ ΔPQN
(ii) ΔABC ≅ ΔPQR
![Ncert solutions class 9 chapter 7-19 Ncert solutions class 9 chapter 7-19](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-19.jpeg)
Given parameters are:
BC = QR and
(i) ½ BC = BM and ½ QR = QN (Since AM and PN are medians)
Also, BC = QR
So, ½ BC = ½ QR
In ΔABM and ΔPQN,
AM = PN and AB = PQ (As given in the question)
BM = QN (Already proved)
∴ ΔABM ≅ ΔPQN by SSS congruency.
(ii) In ΔABC and ΔPQR,
AB = PQ and BC = QR (As given in the question)
∠ABC = ∠PQR (by CPCT)
So, ΔABC ≅ ΔPQR by SAS congruency.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.3-Question-Number-3.jpg)
4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
![Ncert solutions class 9 chapter 7-20 Ncert solutions class 9 chapter 7-20](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-20.jpeg)
It is known that BE and CF are two equal altitudes.
Now, in ΔBEC and ΔCFB,
∠BEC = ∠CFB = 90° (Same Altitudes)
BE = CF (Common side)
So, ΔBEC ≅ ΔCFB by RHS congruence criterion.
Also, ∠C = ∠B (by CPCT)
Therefore, AB = AC as sides opposite to the equal angles is always equal.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Exercise-7.3-Question-Number-4.jpg)
5. ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.
![Ncert solutions class 9 chapter 7-21 Ncert solutions class 9 chapter 7-21](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-21.png)
In the question, it is given that AB = AC
Now, ΔABP and ΔACP are similar by RHS congruency as
∠APB = ∠APC = 90° (AP is altitude)
AP = AP (Common side)
So, ΔABP ≅ ΔACP.
∴ ∠B = ∠C (by CPCT)
Exercise: 7.4 (Page No: 132)
1. Show that in a right-angled triangle, the hypotenuse is the longest side.
![Ncert solutions class 9 chapter 7-22 Ncert solutions class 9 chapter 7-22](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-22.jpeg)
It is known that ABC is a triangle right angled at B.
We know that,
∠A +∠B+∠C = 180°
Now, if ∠B+∠C = 90° then ∠A has to be 90°.
Since A is the largest angle of the triangle, the side opposite to it must be the largest.
So, AB is the hypotenuse which will be the largest side of the above right-angled triangle i.e. ΔABC.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/Show-that-in-a-right-angled-triangle-the-hypotenuse-is-the-longest-side.jpg)
2. In Fig. 7.48, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.
![Ncert solutions class 9 chapter 7-23 Ncert solutions class 9 chapter 7-23](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-23.png)
It is given that ∠PBC < ∠QCB
We know that ∠ABC + ∠PBC = 180°
So, ∠ABC = 180°-∠PBC
∠ACB +∠QCB = 180°
Therefore ∠ACB = 180° -∠QCB
Now, since ∠PBC < ∠QCB,
∴ ∠ABC > ∠ACB
Hence, AC > AB as sides opposite to the larger angle is always larger.
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/12/Q23.jpg)
3. In Fig. 7.49, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.
![Ncert solutions class 9 chapter 7-24 Ncert solutions class 9 chapter 7-24](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-24.png)
In the question, it is mentioned that angles B and angle C is smaller than angles A and D respectively i.e. ∠B < ∠A and ∠C < ∠D.
Since the side opposite to the smaller angle is always smaller
AO < BO — (i)
And OD < OC —(ii)
By adding equation (i) and equation (ii) we get
AO+OD < BO + OC
So, AD < BC
4. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig. 7.50).
Show that ∠A > ∠C and ∠B > ∠D.
![Ncert solutions class 9 chapter 7-25 Ncert solutions class 9 chapter 7-25](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-25.jpeg)
In ΔABD, we see that
AB < AD < BD
So, ∠ADB < ∠ABD — (i) (Since angle opposite to longer side is always larger)
Now, in ΔBCD,
BC < DC < BD
Hence, it can be concluded that
∠BDC < ∠CBD — (ii)
Now, by adding equation (i) and equation (ii) we get,
∠ADB + ∠BDC < ∠ABD + ∠CBD
∠ADC < ∠ABC
Similarly, In triangle ABC,
∠ACB < ∠BAC — (iii) (Since the angle opposite to the longer side is always larger)
Now, In ΔADC,
∠DCA < ∠DAC — (iv)
By adding equation (iii) and equation (iv) we get,
∠ACB + ∠DCA < ∠BAC+∠DAC
⇒ ∠BCD < ∠BAD
∴ ∠A > ∠C
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/AB-and-CD-are-respectively-the-smallest-and-longest-sides-of-a-quadrilateral-ABCD-see-the-given-figure.-Show-that-Angle-A-Grater-than-Angle-C-and-Angle-B-Greater-than-Angle-D.jpg)
5. In Fig 7.51, PR > PQ and PS bisect ∠QPR. Prove that ∠PSR > ∠PSQ.
![Ncert solutions class 9 chapter 7-26 Ncert solutions class 9 chapter 7-26](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-26.jpeg)
It is given that PR > PQ and PS bisects ∠QPR
Now we will have to prove that angle PSR is smaller than PSQ i.e. ∠PSR > ∠PSQ
∠QPS = ∠RPS — (ii) (As PS bisects ∠QPR)
∠PQR > ∠PRQ — (i) (Since PR > PQ as angle opposite to the larger side is always larger)
∠PSR = ∠PQR + ∠QPS — (iii) (Since the exterior angle of a triangle equals to the sum of opposite interior angles)
∠PSQ = ∠PRQ + ∠RPS — (iv) (As the exterior angle of a triangle equals to the sum of opposite interior angles)
By adding (i) and (ii)
∠PQR +∠QPS > ∠PRQ +∠RPS
Thus, from (i), (ii), (iii) and (iv), we get
∠PSR > ∠PSQ
6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
First, let “ l ” be a line segment and “B” be a point lying on it. A line AB perpendicular to l is now drawn. Also, let C be any other point on l . The diagram will be as follows:
![Ncert solutions class 9 chapter 7-27 Ncert solutions class 9 chapter 7-27](https://cdn1.byjus.com/wp-content/uploads/2020/07/ncert-solutions-class-9-chapter-7-27.png)
In ΔABC, ∠B = 90°
Now, we know that
∴ ∠A +∠C = 90°
Hence, ∠C must be an acute angle which implies ∠C < ∠B
So, AB < AC (As the side opposite to the larger angle is always larger)
![case study class 9 maths chapter 7 case study class 9 maths chapter 7](https://cdn1.byjus.com/wp-content/uploads/2021/11/Show-that-of-all-line-segments-drawn-from-a-given-point-not-on-it-the-perpendicular-line-segment-is-the-shortest.jpg)
Summary of NCERT Solutions for Class 9 Maths Chapter 7 Triangles
Triangle is a part of Geometry. However, the complete Geometry of Class 9 constitutes a weightage of 22 marks out of 80 marks. Have a look at the types of questions that are expected from Geometry in the annual exam of class 9 Maths paper.
Introduction to Euclid’s Geometry, Lines and Angles, Triangles, Quadrilaterals, Areas, Circles, Constructions | 4 Qs of 1 mark each | 2 Qs of 3 marks each | 2 Qs of 6 marks each |
Students should practise all the questions from the exercise to score high marks in the Class 9 Maths paper. The step-by-step solution to all the exercises of NCERT Class 9 Maths Chapter 7 is provided below:
In previous classes, students must have used the properties of triangles for solving the questions, but now in the NCERT Textbook of Class 9 Maths Chapter 7, students will learn how to prove these properties. For solving the questions related to this topic, it is very necessary that students should know the congruence rule. First, go through the theory and then look at the solved examples that are already there in the book. After that, start solving the exercise problems.
Students can also have a look at the NCERT Solutions of Class 9 for Science subject to know the answers of all the chapters with a detailed explanation.
Important Concepts Learned in NCERT Class 9 Maths Chapter 7 – Triangles
The aim of including this Triangle Chapter in the Class 9 Maths NCERT textbook is to make students know the following concepts:
- Congruence of triangles.
- Criteria for congruence of triangles (SAS congruence rule, ASA congruence rule, SSS congruence rule, RHS congruence rule).
- Properties of triangles.
- Inequalities of triangles.
We hope this information on “ NCERT Solution Class 9 Maths Chapter 7 ” is useful for students. Click on NCERT Solutions to get the solved answers from the NCERT book for all the classes. Stay tuned for further updates on CBSE and other competitive exams. To access interactive Maths and Science Videos, download BYJU’S App and subscribe to our YouTube Channel.
Triangles is a very important chapter as the fundamental concepts introduced here are carried forward to higher levels of education. For this purpose, after completing the questions from the NCERT Textbook, students are recommended to solve the other textbooks which are prescribed by the CBSE Board.
- RD Sharma Solutions for Class 9 Maths Chapter 9 Triangle and its Angles
Disclaimer:
Dropped Topics – 7.6 Inequalities in triangles.
Frequently Asked Questions on NCERT Solutions for Class 9 Maths Chapter 7
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- NCERT Solutions for Class 9 Maths Chapter 7 Free PDF Download
NCERT Solutions for Class 9 Maths Chapter 7 – Triangles
NCERT Solutions for Class 9 Maths Chapter 7 based on the latest CBSE syllabus provides detailed explanations for all the questions provided in the NCERT textbooks. Our NCERT Solutions are explained step by step which helps you to boost your exam preparations and also help you to understand the concept in a detailed manner.
NCERT Solutions for Class 9 Maths Chapter 7 explains the different dimensions of shapes. These solutions are very interesting and easy to understand. NCERT Solutions for Class 9 Maths Chapter 7 are prepared by our subject experts. In case you have a doubt while you are studying, we have a team of teachers who give live doubt solving session only for you.
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CBSE Class 9 Maths Chapter 7 – Triangles
In NCERT Solutions for Class 9 Maths Chapter 7, you will learn the concept of congruence of triangles, criteria for congruence of triangles (SAS congruence rule, ASA congruence rule, SSS congruence rule, RHS congruence rule), rules of congruence, properties of triangles and the inequalities of a triangle.
Sub-topics covered under NCERT Solutions for Class 9 Maths Chapter 7
7.1 – Introduction
7.2 – Congruence of Triangles
7.3 – Criteria for Congruence of Triangles
7.4 – Some Properties of a Triangle
7.5 – Some More Criteria for Congruence of Triangles
7.6 – Inequalities in a Triangle
7.7 – Summary
NCERT Solutions for Class 9 Maths Chapter 7
In NCERT Solutions for Class 9 Maths Chapter 7, you will learn about the congruence of triangles, properties of triangles, and inequalities of the triangle. Let us now discuss the subtopics included in this Chapter in detail.
In this, you will study in detail the congruence of triangles, properties of triangles and inequalities in a triangle.
In this, you will study about the congruence of a triangle, properties of congruent figures.
In this, you will study the criteria of congruence of triangle SAS congruence rule, ASA congruence rule, AAS congruence rule.
In this, you will study the theorems of a triangle based on congruence of different types of triangle such as angles opposite to equal sides of an isosceles triangle are equal, the opposite sides of equal angles of a triangle are equal.
In this, you will study the criteria of congruence of a triangle with all sides equal, and for right-angled triangle i.e. SSS, RHS.
In this, you will study the various inequalities of a triangle such as an angle opposite to the longer side is larger (greater), the side opposite to the greater angle is greater, the sum of any two sides of a triangle is greater than the third side.
In this, you will get the extract of the chapter and all-important points to be remembered.
You can download NCERT Solutions for Class 9 Maths Chapter 7 for free by clicking on the download button below
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NCERT Solutions for Class 9 Maths Chapter 7 Triangles
Ex 7.2 Class 9 Maths
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1 are part of NCERT Solutions for Class 9 Maths . Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1 Q1](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-Q1.png)
(i) In ∆ ABC and ∆ BAC, AD = BC (Given) ∠DAB = ∠CBA (Given) AB = AB (Common) ∴ ∆ ABD ≅ ∆BAC (By SAS congruence)
(ii) Since ∆ABD ≅ ∆BAC ⇒ BD = AC [By C.P.C.T.]
(iii) Since ∆ABD ≅ ∆BAC ⇒ ∠ABD = ∠BAC [By C.P.C.T.]
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1 Q3](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-Q3.png)
(i) Now, in ∆DAP and ∆EBP, we have ∠PAD = ∠PBE [ ∵∠BAD = ∠ABE] AP = BP [Proved above] ∠DPA = ∠EPB [Proved above] ∴ ∆DAP ≅ ∆EBP [By ASA congruency]
(ii) Since, ∆ DAP ≅ ∆ EBP ⇒ AD = BE [By C.P.C.T.]
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1 Q8](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-Q8.png)
(i) In ∆AMC and ∆BMD, we have CM = DM [Given] ∠AMC = ∠BMD [Vertically opposite angles] AM = BM [Proved above] ∴ ∆AMC ≅ ∆BMD [By SAS congruency]
(ii) Since ∆AMC ≅ ∆BMD ⇒ ∠MAC = ∠MBD [By C.P.C.T.] But they form a pair of alternate interior angles. ∴ AC || DB Now, BC is a transversal which intersects parallel lines AC and DB, ∴ ∠BCA + ∠DBC = 180° [Co-interior angles] But ∠BCA = 90° [∆ABC is right angled at C] ∴ 90° + ∠DBC = 180° ⇒ ∠DBC = 90°
(iii) Again, ∆AMC ≅ ∆BMD [Proved above] ∴ AC = BD [By C.P.C.T.] Now, in ∆DBC and ∆ACB, we have BD = CA [Proved above] ∠DBC = ∠ACB [Each 90°] BC = CB [Common] ∴ ∆DBC ≅ ∆ACB [By SAS congruency]
(iv) As ∆DBC ≅ ∆ACB DC = AB [By C.P.C.T.] But DM = CM [Given] ∴ CM = \(\frac { 1 }{ 2 }\)DC = \(\frac { 1 }{ 2 }\)AB ⇒ CM = \(\frac { 1 }{ 2 }\)AB
NCERT Solutions for Class 9 Maths Chapter 7 Triangles (त्रिभुज) (Hindi Medium) Ex 7.1
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NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2
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(ii) In ∆ABO and ∆ACO, we have AB = AC [Given] ∠OBA = ∠OCA [ ∵\(\frac { 1 }{ 2 }\)∠B = \(\frac { 1 }{ 2 }\)∠C] OB = OC [Proved above] ∆ABO ≅ ∆ACO [By SAS congruency] ⇒ ∠OAB = ∠OAC [By C.P.C.T.] ⇒ AO bisects ∠A.
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2 Q2](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.2-Q2.png)
(ii) Since, ∆ABE ≅ ∆ACF ∴ AB = AC [By C.P.C.T.] ⇒ ABC is an isosceles triangle.
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2 Q5](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.2-Q5.png)
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3
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(ii) In ∆ABP and ∆ACP, we have AB = AC [Given] ∠BAP = ∠CAP [From (1)] ∴ AP = PA [Common] ∴ ∆ABP ≅ ∆ACP [By SAS congruency]
(iii) Since, ∆ABP ≅ ∆ACP ⇒ ∠BAP = ∠CAP [By C.P.C.T.] ∴ AP is the bisector of ∠A. Again, in ∆BDP and ∆CDP, we have BD = CD [Given] DP = PD [Common] BP = CP [ ∵ ∆ABP ≅ ∆ACP] ⇒ A BDP = ACDP [By SSS congruency] ∴ ∠BDP = ∠CDP [By C.P.C.T.] ⇒ DP (or AP) is the bisector of ∠BDC ∴ AP is the bisector of ∠A as well as ∠D.
(iv) As, ∆ABP ≅ ∆ACP ⇒ ∠APS = ∠APC, BP = CP [By C.P.C.T.] But ∠APB + ∠APC = 180° [Linear Pair] ∴ ∠APB = ∠APC = 90° ⇒ AP ⊥ BC, also BP = CP Hence, AP is the perpendicular bisector of BC.
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3 Q2](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.3-Q2.png)
(ii) Since, ∆ABD ≅ ∆ACD, ⇒ ∠BAD = ∠CAD [By C.P.C.T.] So, AD bisects ∠A
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3 Q3](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.3-Q3.png)
(i) In ∆ABM and ∆PQN, we have AB = PQ , [Given] AM = PN [Given] BM = QN [From (3)] ∴ ∆ABM ≅ ∆PQN [By SSS congruency]
(ii) Since ∆ABM ≅ ∆PQN ⇒ ∠B = ∠Q …(4) [By C.P.C.T.] Now, in ∆ABC and ∆PQR, we have ∠B = ∠Q [From (4)] AB = PQ [Given] BC = QR [Given] ∴ ∆ABC ≅ ∆PQR [By SAS congruency]
![case study class 9 maths chapter 7 NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3 Q4](https://www.learncbse.in/wp-content/uploads/2020/10/NCERT-Solutions-for-Class-9-Maths-Chapter-7-Triangles-Ex-7.3-Q4.png)
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4
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NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5
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NCERT Solutions for Class 9 Maths All Chapters
- Chapter 1 Number systems
- Chapter 2 Polynomials
- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations in Two Variables
- Chapter 5 Introduction to Euclid Geometry
- Chapter 6 Lines and Angles
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heron’s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Class 9 Maths (Download PDF)
We hope the NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1, drop a comment below and we will get back to you at the earliest.
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NCERT Solutions for Class 9 Maths Chapter 7 Triangles
Ncert solutions for class 9 maths chapter 7 triangles| pdf download.
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- Exercise 7.1 Chapter 7 Class 9 Maths NCERT Solutions
- Exercise 7.2 Chapter 7 Class 9 Maths NCERT Solutions
- Exercise 7.3 Chapter 7 Class 9 Maths NCERT Solutions
- Exercise 7.4 Chapter 7 Class 9 Maths NCERT Solutions
- Exercise 7.5 Chapter 7 Class 9 Maths NCERT Solutions
NCERT Solutions for Class 9 Maths Chapters:
How many exercises in Chapter 7 Triangles?
Each of the equal angles of an isosceles triangle is 38°, what is the measure of the third angle, find the measure of each of acute angle in a right angle isosceles triangle., if two angles are (30 ∠ a)º and (125 + 2a)º and they are supplement of each other. find the value of ‘a’., contact form.
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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula
Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.
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Class 9 Maths Case Study Questions of Chapter 1 Real Numbers
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Case study Questions in Class 9 Mathematics Chapter 1 are very important to solve for your exam. Class 9 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 9 Maths Case Study Questions Chapter 1 Real Numbers
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In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.
Real Numbers Case Study Questions With Answers
Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 1 Real Numbers
Case Study/Passage-Based Questions
Case Study 1: A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
Observe the following factor tree and answer the following:
1. What will be the value of x?
Answer: b) 13915
2. What will be the value of y?
Answer: c) 11
3. What will be the value of z?
Answer: b) 23
4. According to the Fundamental Theorem of Arithmetic 13915 is a
a) Composite number
b) Prime number
c) Neither prime nor composite
d) Even number
Answer: a) Composite number
5. The prime factorization of 13915 is
a) 5 × 11 3 × 13 2
b) 5 × 11 3 × 23 2
c) 5 × 11 2 × 23
d) 5 × 11 2 × 13 2
Answer: c) 5 × 112 × 23
Case Study 2: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.
(i) For what value of n, 4 n ends in 0?
(a) 10 (b) when n is even (c) when n is odd (d) no value of n
Answer: (d) no value of n3
(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, an is a rational number?
(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0
Answer: (c) for all n > 1
(iii) If x and y are two odd positive integers, then which of the following is true?
(a) x 2 +y 2 is even (b) x 2 +y 2 is not divisible by 4 (c) x 2 +y 2 is odd (d) both (a) and (b)
Answer: (d) both (a) and (b)
(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is
(a) always true (b) always false (c) sometimes true (d) None of these
Answer:(a) always true
(v) If n is any odd integer, then n 2 – 1 is divisible by
(a) 22 (b) 55 (c) 88 (d) 8
Answer: (d) 8
Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Real Numbers 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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Answer: (a) 30 degrees. Q5. The lengths of the two equal sides of the kite triangle are: (a) 3 units each. (b) 4 units each. (c) 5 units each. (d) It cannot be determined. Answer: (c) 5 units each. Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 7 Triangles with ...
Case Study Questions for Class 9 Maths Chapter 7 Triangles Here we are providing case study questions for Class 9 Maths Chapter 7 Triangles. Students are suggested to solve the questions by themselves first and then check the answers. This will help students to check their grasp on this particular chapter Triangles. Case Study Questions: … Continue reading Case Study Questions for Class 9 ...
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.
Introduction of CBSE Case Study Questions for Class 9 Maths - Pdf in English is available as part of our Class 9 preparation & CBSE Case Study Questions for Class 9 Maths - Pdf in Hindi for Class 9 courses. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Class 9 Mathematics Case study question 2. Read the Source/Text given below and answer any four questions: Maths teacher draws a straight line AB shown on the blackboard as per the following figure. Now he told Raju to draw another line CD as in the figure. The teacher told Ajay to mark ∠ AOD as 2z.
In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are ... Chapter-7(Alternating Current) Chapter-8(Electromagnetic Waves) Chapter-9(Ray Optics and Optical Instruments) Chapter-10(Wave Optics) Chapter-11(Dual Nature of Radiation and Matter)
Case Study Questions for Chapter 15 Probability. The above Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.
Case-Based Questions | Triangles [Class 9 Maths Chapter 7] NCERT Solutions | Jyotsana Mam | Vedantu. This is a Super Amazing Session with Our Master Teacher ...
5. (a) Aditya is a Class IX student residing in a village. One day, he went to a city Hospital along with his grandfather for general checkup. From there he visited three places - School, Library and Police Station. After returning to his village, he plotted a graph by taking Hospital as origin and marked three places on the graph as per his ...
CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions. Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation. Case Study Questions.
Important Questions for CBSE Class 9 Chapter 7 -Triangles are provided here by our experts, along with their solutions. These questions are extracted from the NCERT book as per CBSE syllabus.Students who are preparing for standard 9 Maths final exam (2022 - 2023) should practise these questions to score excellent marks.. Solve extra questions along with important questions for class 9 Maths ...
Here you will get complete NCERT Solutions for Class 9 Maths Chapter 7 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.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles, covers key concepts and proofs for different triangle properties. Download FREE PDF solved by master teachers updated for the year 2024-25 ... Learning about triangles is important because they are a basic shape used in many aspects of mathematics and everyday life. Also study ...
According to Chapter 7 of Class 9 Maths, we need at least one of the following information to construct a triangle: Length of all three sides. Length of two sides and included angle. The measurement of any two angles and the included side. The length of the hypotenuse and one side in case of a right triangle.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles provides the answers and questions related to the chapter as included in the CBSE Syllabus for 2023-24. The word triangle itself describes its meaning. "Tri" means "three",; so a closed figure formed by three intersecting lines is known as a Triangle. Students must have already ...
In NCERT Solutions for Class 9 Maths Chapter 7, you will learn about the congruence of triangles, properties of triangles, and inequalities of the triangle. Let us now discuss the subtopics included in this Chapter in detail. 7.1 - Introduction. In this, you will study in detail the congruence of triangles, properties of triangles and ...
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3. Ex 7.3 Class 9 Maths Question 1. ∆ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see figure). If AD is extended to intersect BC at P, show that. (iv) AP is the perpendicular bisector of BC.
Find the measure of each of acute angle in a right angle isosceles triangle. Let the measure of each of the equal acute angle of the Δ be x. ∴ We have: x + x + 90° = 180°. ⇒ x + x = 180° - 90° = 90°. ⇒ x= (90°/2)= 45°. If two angles are (30 ∠ a)º and (125 + 2a)º and they are supplement of each other.
January 7, 2023 July 29, 2023 Physics Gurukul 4 Comments on Case Study Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables. ... Case Study Questions for Class 9 Science Chapter 1 Matter in Our Surroundings; An Imperial Capital - Vijayanagara Assertion Reason Questions for CBSE Class 12 History Chapter 7 ...
Maths Case-Study Qs. Maths Case-Study Qs. VIEW ALL. TopperLearning offers an online platform to access case studies for CBSE Class 9 students. Explore your analytical and problem-solving skills by solving case studies with our expert guidance. Get started today!
Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 2 Polynomials. Case Study/Passage Based Questions. Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p (x) = 4x 2 + 12x + 5, which is the product of their individual shares.
He paid 110 for 4 notebooks and 3 pens. Later, Deepak guesses the cost of one pen is Rs. 10 and Lohith guess the cost of one notebook is Rs. 30. (i) Form the pair of linear equations in two variables from this situation by taking the cost of one notebook as Rs. x and the cost of one pen as Rs. y. (a) 3x + 2y = 80 and 4x + 3y = 110.
5. The prime factorization of 13915 is. a) 5 × 11 3 × 13 2. b) 5 × 11 3 × 23 2. c) 5 × 11 2 × 23. d) 5 × 11 2 × 13 2. Show Answer. Case Study 2: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment ...