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CBSE Case Study Questions Class 9 Maths Chapter 7 Triangles PDF Download

Case Study Questions Class 9 Maths Chapter 7   are very important to solve for your exam. Class 9 Maths Chapter 7 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 7 Triangles

Case Study Questions Class 9 Maths Chapter 7 Triangles

Case Study 1. A group of students is studying the properties of triangles. They came across the following scenario:

Three friends, Ankit, Bhavna, and Chetan, were discussing their recent hiking trip. During their hike, they noticed a triangular-shaped lake. They observed the following:

• The lake has three sides of different lengths.
• The sum of the lengths of any two sides of the lake is greater than the length of the third side.
• The largest angle of the lake is less than 90 degrees.
• The smallest angle of the lake is greater than 30 degrees.

Based on this information, the students were asked to analyze the properties of the triangle formed by the lake. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The type of triangle formed by the lake is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (c) Scalene

Q2. The sum of the measures of the three angles of the lake’s triangle is: (a) 180 degrees (b) 90 degrees (c) 360 degrees (d) It cannot be determined

Answer: (a) 180 degrees

Q3. The lake’s triangle is an example of a triangle that satisfies the: (a) Angle-side-angle (ASA) condition (b) Side-angle-side (SAS) condition (c) Side-side-side (SSS) condition (d) None of the above

Answer: (c) Side-side-side (SSS) condition

Q4. The measure of the largest angle of the lake’s triangle is: (a) 30 degrees (b) 60 degrees (c) 90 degrees (d) More than 90 degrees

Answer: (c) 90 degrees

Q5. The measure of the smallest angle of the lake’s triangle is: (a) 30 degrees (b) 60 degrees (c) 90 degrees (d) Less than 30 degrees

Answer: (d) Less than 30 degrees

Case Study 2. A group of students is studying the properties of triangles. They encountered the following scenario:

Three friends, Rahul, Sana, and Tina, participated in a kite-flying competition. They noticed that their kites formed a triangular shape in the sky. They made the following observations:

• The lengths of two sides of the kite triangle are equal.
• The measure of the largest angle of the kite triangle is 90 degrees.
• The sum of the measures of the three angles of the kite triangle is 180 degrees.
• The lengths of the three sides of the kite triangle are in the ratio 3:4:5.

Based on this information, the students were asked to analyze the properties of the triangle formed by their kites. Let’s see if you can answer the questions correctly:

Q1. The type of triangle formed by their kites is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (b) Isosceles

Q2. The length of the third side of the kite triangle is: (a) 3 units (b) 4 units (c) 5 units (d) It cannot be determined

Answer: (c) 5 units

Q3. The kite triangle is an example of a triangle that satisfies the: (a) Angle-side-angle (ASA) condition (b) Side-angle-side (SAS) condition (c) Side-side-side (SSS) condition (d) None of the above

Answer: (b) Side-angle-side (SAS) condition

Q4. The measure of the smallest angle of the kite triangle is: (a) 30 degrees (b) 45 degrees (c) 60 degrees (d) 90 degrees

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 Answers Pdf free download has been useful to an extent. If you have any other queries about Case Study Questions Class 9 Maths Chapter 7 Triangles and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible.

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Case Study Questions for Class 9 Maths Chapter 7 Triangles

• Last modified on: 8 months ago
• Reading Time: 6 Minutes

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:

Questions 1:

In a park, there are two triangular flower beds. Flower bed ABC has sides AB = 8 cm, BC = 6 cm, and CA = 10 cm. Flower bed PQR has sides PQ = 8 cm, QR = 10 cm, and RP = 6 cm.

(i) Using the given information, can we conclude that flower bed ABC is congruent to flower bed PQR? Why or why not? a) Yes, because all three sides of ABC are equal to the corresponding sides of PQR. b) Yes, because all three angles of ABC are equal to the corresponding angles of PQR. c) No, because the sides and angles of ABC and PQR are not equal. d) Yes, because ABC and PQR are both triangular flower beds.

(ii) If angle A = 40° and angle B = 60° in flower bed ABC, what is the measure of angle C? a) 40° b) 60° c) 80° d) 100°

(iii) In flower bed ABC, a new side AD is added such that AD = 8 cm. Now, can we conclude that triangle ABD is congruent to triangle PQR? Why or why not? a) Yes, because all three sides of ABD are equal to the corresponding sides of PQR. b) Yes, because all three angles of ABD are equal to the corresponding angles of PQR. c) No, because the sides and angles of ABD and PQR are not equal. d) Yes, because both triangles have a side of 8 cm.

(iv) If angle P = 50° and angle Q = 70° in flower bed PQR, what is the measure of angle R? a) 50° b) 70° c) 90° d) 110°

(v) Suppose flower bed ABC is shifted to a new location within the park without changing its shape or size. In this new location, is flower bed ABC congruent to its original position? Why or why not? a) Yes, because the shape and size of ABC remain the same. b) No, because the location of ABC has changed. c) Yes, because the park remains the same. d) No, because the other flower bed PQR is not shifted.

(i) c) No, because the sides and angles of ABC and PQR are not equal.

(ii) c) 80°

(iii) b) Yes, because all three angles of ABD are equal to the corresponding angles of PQR.

(iv) d) 110°

(v) a) Yes, because the shape and size of ABC remain the same.

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Case Study Questions for Class 9 Maths

• Post author: studyrate
• Post published:
• Post category: class 9th
• Post comments: 0 Comments

Are you preparing for your Class 9 Maths board exams and looking for an effective study resource? Well, you’re in luck! In this article, we will provide you with a collection of Case Study Questions for Class 9 Maths specifically designed to help you excel in your exams. These questions are carefully curated to cover various mathematical concepts and problem-solving techniques. So, let’s dive in and explore these valuable resources that will enhance your preparation and boost your confidence.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

CBSE Class 9 Maths Board Exam will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 9  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

Table of Contents

CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution

Case study questions are a form of examination where students are presented with real-life scenarios that require the application of mathematical concepts to arrive at a solution. These questions are designed to assess students’ problem-solving abilities, critical thinking skills, and understanding of mathematical concepts in practical contexts.

Chapterwise Case Study Questions for Class 9 Maths

Case study questions play a crucial role in the field of mathematics education. They provide students with an opportunity to apply theoretical knowledge to real-world situations, thereby enhancing their comprehension of mathematical concepts. By engaging with case study questions, students develop the ability to analyze complex problems, make connections between different mathematical concepts, and formulate effective problem-solving strategies.

• 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 Quadilaterals
• 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

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.

• Class 9 Science Case Study Questions
• Class 9 Social Science Case Study Questions

How to Approach Case Study Questions

When tackling case study questions, it is essential to adopt a systematic approach. Here are some steps to help you approach and solve these types of questions effectively:

• Read the case study carefully: Understand the given scenario and identify the key information.
• Identify the mathematical concepts involved: Determine the relevant mathematical concepts and formulas applicable to the problem.
• Formulate a plan: Devise a plan or strategy to solve the problem based on the given information and mathematical concepts.
• Solve the problem step by step: Apply the chosen approach and perform calculations or manipulations to arrive at the solution.
• Verify and interpret the results: Ensure the solution aligns with the initial problem and interpret the findings in the context of the case study.

Tips for Solving Case Study Questions

Here are some valuable tips to help you effectively solve case study questions:

• Read the question thoroughly and underline or highlight important information.
• Break down the problem into smaller, manageable parts.
• Visualize the problem using diagrams or charts if applicable.
• Use appropriate mathematical formulas and concepts to solve the problem.
• Show all the steps of your calculations to ensure clarity.
• Check your final answer and review the solution for accuracy and relevance to the case study.

Benefits of Practicing Case Study Questions

Practicing case study questions offers several benefits that can significantly contribute to your mathematical proficiency:

• Enhances critical thinking skills
• Improves problem-solving abilities
• Deepens understanding of mathematical concepts
• Develops analytical reasoning
• Prepares you for real-life applications of mathematics
• Boosts confidence in approaching complex mathematical problems

Case study questions offer a unique opportunity to apply mathematical knowledge in practical scenarios. By practicing these questions, you can enhance your problem-solving abilities, develop a deeper understanding of mathematical concepts, and boost your confidence for the Class 9 Maths board exams. Remember to approach each question systematically, apply the relevant concepts, and review your solutions for accuracy. Access the PDF resource provided to access a wealth of case study questions and further elevate your preparation.

Q1: Can case study questions help me score better in my Class 9 Maths exams?

Yes, practicing case study questions can significantly improve your problem-solving skills and boost your performance in exams. These questions offer a practical approach to understanding mathematical concepts and their real-life applications.

Q2: Are the case study questions in the PDF resource relevant to the Class 9 Maths syllabus?

Absolutely! The PDF resource contains case study questions that align with the Class 9 Maths syllabus. They cover various topics and concepts included in the curriculum, ensuring comprehensive preparation.

Q3: Are the solutions provided for the case study questions in the PDF resource?

Yes, the PDF resource includes solutions for each case study question. You can refer to these solutions to validate your answers and gain a better understanding of the problem-solving process.

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• CBSE Maths Important Questions
• Class 9 Maths
• Chapter 7: Triangles

Important Questions CBSE Class 9 Maths Chapter 7- Triangles

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 to have a better practice and brief revision before the examination. The questions in Chapter 7, triangles, are majorly based on congruency or similarity of triangles. Solving these questions will give students an idea of the types of questions asked in the exam.

Also Check:

• Important 2 Marks Questions for CBSE 9th Maths
• Important 3 Marks Questions for CBSE 9th Maths
• Important 4 Marks Questions for CBSE 9th Maths

Important Questions & Solutions For CBSE Class 9 Chapter 7 (Triangles)

Q.1: ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that

(i) ΔABD ≅ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

As per given in the question,

∠DAB = ∠CBA and AD = BC.

(i) ΔABD and ΔBAC are similar by SAS congruency as

AB = BA (common arm)

∠DAB = ∠CBA and AD = BC (given)

So, triangles ABD and BAC are similar

i.e. ΔABD ≅ ΔBAC. (Hence proved).

(ii) As it is already proved,

ΔABD ≅ ΔBAC

BD = AC (by CPCT)

(iii) Since ΔABD ≅ ΔBAC

So, the angles,

∠ABD = ∠BAC (by CPCT).

Q.2: AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

Given, AD and BC are two equal perpendiculars to AB.

To prove: CD is the bisector of AB

Triangles ΔAOD and ΔBOC are similar by AAS congruency

(i) ∠A = ∠B (perpendicular angles)

(ii) AD = BC (given)

(iii) ∠AOD = ∠BOC (vertically opposite angles)

∴ ΔAOD ≅ ΔBOC.

So, AO = OB ( by CPCT).

Thus, CD bisects AB (Hence proved).

Q.3: 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. Show that:

(i) ΔAPB ≅ ΔAQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

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 (both are right angles)

AB = AB (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, we can say point B is equidistant from the arms of ∠A.

Q.4: 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. Show that

(i) ΔDAP ≅ ΔEBP

(ii) AD = BE

Given, P is the mid-point of line segment AB.

Also, ∠BAD = ∠ABE and ∠EPA = ∠DPB

(i) Given, ∠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 (given)

So, by ASA congruency criterion,

ΔDAP ≅ ΔEBP.

(ii) By the rule of CPCT,

Q.5: 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 the figure). Show that:

(i) ΔAMC ≅ ΔBMD

(ii) ∠DBC is a right angle.

(iii) ΔDBC ≅ ΔACB

(iv) CM = 1/2 AB

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)

∠CMA = ∠DMB (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 (Both 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

Q.6: ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal.

(i) BE and CF are altitudes.

(ii) AC = AB

Triangles ΔAEB and ΔAFC are similar by AAS congruency, since;

∠A = ∠A (common arm)

∠AEB = ∠AFC (both are right angles)

AB = AC (Given)

∴ ΔAEB ≅ ΔAFC

and BE = CF (by CPCT).

Q.7: ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle.

Given, AB = AC and AD = AB

To prove: ∠BCD is a right angle.

Consider ΔABC,

Also, ∠ACB = ∠ABC (Angles opposite to equal sides)

Now, consider ΔACD,

Also, ∠ADC = ∠ACD (Angles opposite to equal sides)

∠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°

Q.8: 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 the figure). 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.

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:

AD = AD (It is the common arm)

AB = AC (Since ΔABC is isosceles)

BD = CD (Since ΔDBC is isosceles)

∴ ΔABD ≅ ΔACD.

(ii) ΔABP and ΔACP are similar as:

AP = AP (common side)

∠PAB = ∠PAC ( by CPCT since ΔABD ≅ ΔACD)

So, ΔABP ≅ ΔACP by SAS congruency.

(iii) ∠PAB = ∠PAC by CPCT as ΔABD ≅ ΔACD.

AP bisects ∠A. ………… (1)

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. ……………. (2)

Now by comparing equation (1) and (2) it can be said that AP bisects ∠A as well as ∠D.

(iv) ∠BPD = ∠CPD (by CPCT as ΔBPD ≅ ΔCPD)

and BP = CP — (1)

∠BPD + ∠CPD = 180° (Since BC is a straight line.)

⇒ 2∠BPD = 180°

⇒ ∠BPD = 90° —(2)

Now, from equations (1) and (2), it can be said that

AP is the perpendicular bisector of BC.

Q.9: 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 the figure). Show that:

(i) ΔABM ≅ ΔPQN

(ii) ΔABC ≅ ΔPQR

BC = QR and

(i) 1/2 BC = BM and 1/2QR = QN (Since AM and PN are medians)

Also, BC = QR

So, 1/2 BC = 1/2QR

In ΔABM and ΔPQN,

AM = PN and AB = PQ (Given)

BM = QN (Already proved)

∴ ΔABM ≅ ΔPQN by SSS congruency.

(ii) In ΔABC and ΔPQR,

AB = PQ and BC = QR (Given)

∠ABC = ∠PQR (by CPCT)

So, ΔABC ≅ ΔPQR by SAS congruency.

Q.10: In the Figure, PR > PQ and PS bisect ∠QPR. Prove that ∠PSR > ∠PSQ.

Given, PR > PQ and PS bisects ∠QPR

To prove: ∠PSR > ∠PSQ

∠QPS = ∠RPS — (1) (PS bisects ∠QPR)

∠PQR > ∠PRQ — (2) (Since PR > PQ as angle opposite to the larger side is always larger)

∠PSR = ∠PQR + ∠QPS — (3) (Since the exterior angle of a triangle equals the sum of opposite interior angles)

∠PSQ = ∠PRQ + ∠RPS — (4) (As the exterior angle of a triangle equals to the sum of opposite interior angles)

By adding (1) and (2)

∠PQR + ∠QPS > ∠PRQ + ∠RPS

Now, from (1), (2), (3) and (4), we get

∠PSR > ∠PSQ.

Video Lesson on Congruent Triangles

Extra Questions for Class 9 Maths Triangles Chapter 7

• Two adjacent angles on a straight line are in a ratio 5:4. Find the measure of each one of these angles. (Answer: 100 ° and 80 °degree).
• Prove that bisectors of two adjacent supplementary angle include a right angle.
• If two straight lines are perpendicular to the same line, prove that they are parallel to each other.
• The angles of the triangle are in the ratio 2:3:7. Find the measure of each angle of the triangle. (Answer: 30°, 45° and 105°)
• In triangle ABC , ∠A – ∠B = 33 degree and ∠B – ∠C = 180 degree.Find the measure of each angle of the triangle. ( Answer: ∠A = 88° and ∠B = 55° and ∠C = 37°).
• Of the three angles of the triangle, one is twice the smallest and another one is thrice the smallest. Find the angles.  (Answer: 60°, 90°, 30°)
• If each of a triangle is less than the sum of the other two, show that the triangle is acute-angled.
• The sum of two angles of a triangle is 116° and their difference is 24. Find the measure of each angle of the triangle. (Answer: 46°, 70 °, 64°) .
• Two straight lines AB and CD cut each other at O. if angle BOD = 63° then find angle BOC. (Answer: 117°) .
• Two complementary angles are such that twice the measure of the one is equal to three times the measure of the other. The larger of the two measures is. (Answer: 54°) .
• Show that of all line segments drawn from a given point, not on it, the perpendicular line segment is the shortest.
•  If the diagonals of the rectangle ABCD intersect at O and  ∠COD = 78°, then ∠OAB is:

        d) 110 o

     13.  The measure of an angle is twice the measure of supplementary angle. What is the measure of angles?

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Chapter 7 Class 9 Triangles

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Updated for new NCERT Books (for 2023-24 Exams)

NCERT Solutions of Chapter 7 Class 9 Triangles is available free at teachoo. Solutions to all exercise questions, examples and theorems is provided with video of each and every question.

Let's see what we will learn in this chapter. The topics in the chapter are - 

• What is congruency of figures
• Naming of triangles when two triangles are congruent
• What is CPCT - Corresponding Parts of Congruent Triangles
• SAS (Side Angle Side) Congruence Rule (this is without proof)
• ASA (Angle Side Angle) congruence rule with proof (Theorem 7.1)
• Is ASA and AAS congruency the same ?
• Angles opposite to equal sides is equal (Isosceles Triangle Property)
• SSS (Side Side Side) congruence rule with proof (Theorem 7.4)
• RHS (Right angle Hypotenuse Side) congruence rule with proof (Theorem 7.5)
• Angle opposite to longer side is larger, and Side opposite to larger angle is longer
• Triangle Inequality - Sum of two sides of a triangle is always greater than the third side

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