NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.2) Exercise 7.2

NCERT books are the main textbooks used by CBSE Board students, and with good use, students can be well-prepared for their future ventures. For students, NCERT books are quite beneficial and provide a range of advantages for increasing their basic knowledge. The development of a deep comprehension of the fundamental ideas in every subject is supported by NCERT books. The concepts may be properly understood by students by attentively reading the NCERT textbooks. Students will be able to solve problems successfully and effectively once they acquire the necessary conceptual clarity, and there will be long-term academic advantages. If a student could understand a concept, there would be no need for retention. Students may get assistance from the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2, if they have any questions. Students who intend to take competitive examinations can use the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. NCERT books are written with the idea of what students’ minds can comprehend at a certain age and are patterned accordingly. The Extramarks online learning platform has assembled NCERT Solutions to support students in their academic endeavours while keeping in mind the structure of NCERT books.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.2) Exercise 7.2 

Students in Class 9 may quickly download the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 from the Extramarks website or mobile application so they can see and revise the answers to Exercise 7.2 Class 9 Maths even when they are not online. Additionally, NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 will aid in their comprehension of the exercises.

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Access NCERT Solutions for Class 9 Maths Chapter 7 – Triangles

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NCERT textbooks are designed to help students grow intellectually. The Extramarks online learning platform has assembled NCERT solutions to support students in their academic endeavours while keeping in mind the structure of NCERT books. Mathematics concepts are also used in physics, chemistry, economics, engineering, and other academic disciplines.  To fully comprehend some topics pertaining to these disciplines, an understanding of mathematics is required. Forms, shapes, sizes, degrees, temperatures, finance, time, and timepieces are all constituent themes of the academic discipline of mathematics. In some curricula, mathematics is taught as an “instrumental subject” to support the study of other disciplines, while in others, integrated courses that merge mathematics and other subjects are available.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.2

Significant characteristics of Triangles and associated theorems are covered in NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. Due to the fact that this topic involves more proving than solving, a majority of students find it tedious. Students will begin to show interest in it if they can relate the characteristics of Triangles to the examples and comprehend them. For the convenience of students, Extramarks has provided the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2, on their website and learning app. Students may quickly comprehend the process for answering the problems after reading the solutions. Extramarks’ skilled teachers have prepared the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2.

The NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 are very important to refer to if students feel that questions are more challenging than expected. There are a total of 5 exercises in chapter 7 and an optional exercise as well. In Class 9 Maths Chapter 7 Exercise 7.1, there is a total of 8 questions, then in NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2, solutions have been provided for a total of 8 questions as well. In the NCERT Class 9 Maths Chapter 7 Exercise 7.3, there are a total of 5 questions, further, in NCERT Class 9 Maths Chapter 7 Exercise 7.4, there are a total of 6 questions. At last in the Class 9 Maths Chapter 7 Exercise 7.5, there are a total of 4 questions. All of these questions have been solved with precision and expertise in the reference material prepared by Extramarks. Students can rely on the Extramarks e-learning platform undoubtedly. The solutions for each exercise are available on the Extramarks website and students are advised to access these for their academic development.

NCERT Solutions for Class 9

Students get access to a range of study resources through NCERT Solutions for Class 9. All of the course materials are available on the Extramarks website and mobile application. As a result, it is advised that students search the Extramarks website for any relevant queries they might have regarding the chapter. Students may also access the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. They are able to find notes, important problems, and sample papers pertaining to Class 9 Maths Chapter 7 Exercise 7.2. Students may access past years’ papers and get help figuring out their responses by using the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2.

All the other chapters’ NCERT solutions for Class 9 are also available on the Extramarks website and mobile application.

Chapter 1 Number System

Chapter 2 Polynomials

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equations in Two Variables

Chapter 5 Introduction to Euclids 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

CBSE Study Materials for Class 9

Exceptionally proficient instructors of Mathematics have created the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 with accuracy and precision so that students would not encounter any issues when attempting to answer any question.  The Extramarks website offers all Class 9 study resources, all of which were created by experts in their respective fields. At their respective convenience, students may use the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 to swiftly and simply get the solutions to any queries. Students may access academic courses for Class 9 in Mathematics, Science, English, Hindi, and other subjects through the Extramarks website.

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CBSE Study Materials

NCERT is the leading management and research organisation in the country. While it is feasible to pass the CBSE examinations with enough scores by studying the NCERT books, doing so could sometimes be difficult for students who follow the CBSE board curriculum. Students who try to complete exercises from the NCERT Mathematics textbook may find it challenging. Extramarks strictly adheres to the CBSE format. Each chapter is followed by an exercise that must be solved and practised. Students should be informed that Extramarks, where they can also get CBSE study materials, provides access to NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. With the use of Extramarks, any solution is available, like the solutions to Class 9 Maths Ex 7.2.

For students to learn and prepare for the examination more effectively, Extramarks offers CBSE study resources that are developed in an engaging, and student-friendly manner. Subject experts have created the material with sharpness and accuracy so that students can rely on NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. The online study resources, which include syllabi, books, sample papers, past years’ papers, NCERT solutions, NCERT Exemplars, important questions, and CBSE notes, are beneficial for all students. These study materials can help students easily get ready for their examinations.

Q.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.


Ans

Given: In ΔABC, AB=AC and bisectors of ∠B and ∠C intersect        at O.To Prove: (i) OB=OC (ii) AO bisects∠AProof:(i) In ΔABC, AB=AC So,   ∠ACB=∠ABC       [Opposite angles of equal sides are equal.]⇒    12∠ACB=12∠ABC⇒      ∠OCB=∠OBC        [Given, as OB and OC are angle bisectors.]⇒  OB=OC             [Opposite angles of equal sides are equal.]

(ii) In ΔOAB and ΔOAC,  OA=OA            [Common]  AB=AC            [Given]  OB=OC           [Proved above]∴             ΔOAB≅ ΔOAC       [By S.S.S.]Hence,    ∠OAB=∠OAC        [By C.P.C.T.]Thus, OA bisects ∠A.

Q.2 In Δ ABC, AD is the perpendicular bisector of BC (see figure below). Show that Δ ABC is an isosceles triangle in which AB = AC.


Ans

Given: In ΔABC, BD=DC and AD⊥BC.To Prove: AB=ACProof: In ΔABD and ΔACD    AD=AD                [Common]        ∠ADB=∠ADC            [Given]     BD=DC                 [Given]∴      ΔABD ≅ ΔACD            [By S.A.S.]∴            AB=AC                 [By C.P.C.T.]Therefore, ΔABC is isosceles triangle.

Q.3 ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see figure below). Show that these altitudes are equal.


Ans

Given:In ΔABC, AC=AB, BE⊥AC and CF⊥AB.To prove: BE=CF        Proof:In ΔABE and ΔACF    ∠BAE=∠CAF         [Common angle]    ∠BEA=∠CFA         [Each 90°]AB=AC            [Given]∴    ΔABE≅ ΔACF          [By A.A.S.]∴BE=CF            [By C.P.C.T.]                            Hence proved.

Q.4

ABC is a triangle in which altitudes BE and CF to sides ACand AB are equal (see figure below).Show that(i) ΔABE≅ΔACF(ii) AB=AC,i.e.,ABC is an isosceles triangle.

Ans

 Given:In ΔABC, BE=CF, BE⊥AC and CF⊥AB.To prove: (i) ΔABE≅ΔACF            (ii) AB=AC,i.e.,ABC is an isosceles triangle.        Proof:(i) In ΔABE and ΔACF    ∠BAE=∠CAF         [Common angle]    ∠BEA=∠CFA         [Each 90°]BE=CF              [Given]∴    ΔABE≅ ΔACF          [By A.A.S.](ii) AB=AC                  [By C.P.C.T.]i.e.,ABC is an isosceles triangle.                              Hence proved.

Q.5 ABC and DBC are two isosceles triangles on the same base BC (see figure below). Show that ∠ABD = ∠ACD.


Ans

  Given:In ΔABC, AB=AC and in ΔDBC, DB=DC.To prove: ∠ABD=∠ACD        Proof:In ΔABCAB=AC            [Given]∴    ∠ACB= ∠ABC  ...(i)    [Opposite angles of equal sides are equal.]In ΔDBCDB=DC            [Given]∴    ∠DCB= ∠DBC  ...(ii)  [Opposite angles of equal sides are equal.]Adding equation(i) and equation(ii),we get∠ACB +∠DCB= ∠ABC+∠DBC∴      ∠ACD= ∠ABD⇒            ∠ABD=∠ACD                                    Hence proved.

Q.6 ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure below). Show that ∠BCD is a right angle.


Ans

Given:In​ ΔABC, AB=AC, side BA​ is produced to D such that      AD=AB.To prove:∠BCD is a right angle.Proof:In ΔABC,     AB=AC        [Given]∠ACB=∠ABC     [Opposite angles of equal sides are equal.]    =x  (let)            In ΔACD,     AC=AD        [Given]∠ADC=∠ACD     [Opposite angles of equal sides are equal.]    =y  (let)Now, In ΔBCD∠BCD+∠CBD+∠BDC=180°                   (x+y)+x+y=180°           2(x+y)=180°    (x+y)=180°2    ∠BCD=90°⇒∆BCD is right triangle.

Q.7 ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Ans

  Given :In ΔABC, ∠A=90° and AB=AC.To find : ∠ B and∠ C        Sol : In ΔABC,                    AB=AC           [Given]So,        ∠ACB=∠ABC=x    (let)Since,   ∠A+∠B+∠C=180°     90°+x+x=180°2x=180°−90°  x=90°2=45°So, ∠B=45° and ∠C=45°.

Q.8 Show that the angles of an equilateral triangle are 60° each.

Ans

Given : ΔABC is an equilateral triangle.To prove : ∠A=∠B=∠C=60°Proof: In ΔABC,        AB=AC        [Given]

           ∠C=∠B    ...(i)     [Angles opposite to equal sides are equal.] AB=BC            [Given]          ∠C=∠A    ...(ii)    [Angles opposite to equal sides are equal.]By angle sum property in a triangle,∠A+∠B+∠C=180°∠C+∠C+∠C=180°        [From equation (i) and equation(ii)]3∠C=180°  ∠C=180°3=60°So, ∠A =60° and ∠B =60°Therefore, each angle of an equilateral triangle is 60° each.

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1. How can students access NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2?

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2. Are the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 in accordance with the recent syllabus of Mathematics Class 9?

Yes, the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 are produced while keeping in mind the CBSE Class 9 updated syllabus. It is essential to note that Extramarks keeps track of new and added topics in the syllabus so that students would not have confusion. Therefore, students can also find the updated syllabus on the Extramarks website.

3. How can the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2 assist with Class 9 examination preparation?

Students may succeed in the annual examinations of Class 9 and master the academic content by practising the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.2. These answers were developed using the most recent CBSE syllabus, including all the important subject material. Thus, answering these questions will boost students’ confidence as they prepare for their board examinations. Additionally, it helps the students become accustomed to responding to inquiries of varying degrees of complexity. The use of these solutions for reference and preparation for the examinations is strongly advised for students.