NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.1

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Mathematics is an integral part of human thought and logic and is integral to students’ attempts to understand the world and themselves. As well as building mental discipline, it promotes logical reasoning and problem-solving abilities. Moreover, Mathematics is crucial to understanding other school subjects, such as Science, Social Science, and even Music and Art.

In order to determine quantitative solutions to experimental laws, scientists use the fundamentals of Mathematics. It is used in a variety of fields, including Finance, Medicine, Computer Science, Social Sciences, Natural Sciences, and Engineering. So, the concepts of Mathematics are incorporated into the curriculum of all subjects in higher education. Class 9 Mathematics introduces students to many essential concepts of the subject, which form the basis for higher education. To perform well in the examinations and be able to apply those concepts in their future studies, students in Class 9 should develop strong concepts in mathematics.

Chapter 7: Class 9 Mathematics is Triangles. In lower grades, students have seen a glimpse of this chapter. There is no substitute for diligent practice when it comes to Mathematics. NCERT structures the fundamentals of all the subjects. Therefore, Extramarks provides students with r so that they do not have to look elsewhere for properly detailed and easy solutions. Class 9 is an essential academic year in the academic career of students. Besides preparing students for their examinations, the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 provide them with the foundation for academic success. Students must develop comprehensive learning habits in Class 9, which helps them perform better in the Class 10 board examinations. In order to improve students’ academic performance and have a bright academic career, Extramarks provides them with Exercise 7.1 Class 9 Maths NCERT Solutions.

Multiple public and private schools in India are managed and controlled by the Central Board of Secondary Education. Most of the schools in the country follow this board of education, making it one of the most important boards of education in the country. By resolution of the Indian government, the CBSE Board was established in 1929. Schools affiliated with this educational board follow the NCERT curriculum. NCERT promotes and coordinates research related to school education and prepares and publishes model textbooks, supplementary materials, etc. Additionally, it serves as a clearinghouse for ideas and information related to school education, as well as a government agency dedicated to achieving universal elementary education goals. Founded in 1961 by the Government of India, the National Council of Educational Research and Training (NCERT) assists the Central and State Governments with educational policies and programmes.

NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.1 Triangles

Using Extramarks, students can have access to trustworthy NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, without having to search anywhere else. To clear all the queries and doubts of students, the Extramarks website offers multiple learning modules such as K12 Study Material, Live Doubt Solving Sessions, Learn Practice Tests, In-depth Performance Reports and so much more. This allows them to concentrate on their academic goals and succeed in their examinations. Extramarks’ NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 provides students with a deeper understanding of the concepts of the chapter. It allows students to solve any complex problem related to the concepts of the chapter. Whether it is a school examination, a board examination, or a competitive examination, students can score well in any examination with the help of Extramarks. It also provides students with the NCERT solutions for all the academic sessions and subjects, along with the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1.

Access NCERT Answers for Class-9 Maths Chapter 7 – Triangles

The Extramarks website is an online portal dedicated to helping students achieve their full potential. Students have access to so many learning modules that make learning easier and more enjoyable. Extramarks provide students with in-depth performance reports to track their academic progress, Doubt Solving Sessions, Live Classes from top faculty, K12 Study Materials, and much more. Furthermore, the website provides students with reliable study materials such as the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1. These solutions provide step-by-step detailed answers to all the questions of the students. Practising the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, on a regular basis can help students improve their mathematical skills and gain a better command of the subject.

Students can also access several sample papers and past years’ papers on Extramarks, along with the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1. With the guidance of these solutions, students can gain a better understanding of the blueprint of the question paper of the examination and also practice time management, which is very important for the examination. Students can familiarise themselves with the examination pattern as well as the types of questions that can appear in the examinations through past years’ papers. Moreover, they also explain to them the manner in which the answers should be written in the examination. This way, students are able to solve their question papers more efficiently. In addition, sample papers provide students with a breakdown of chapter weightage and marks distribution. As a result, they do not face any last-minute challenges during the examination.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.1) Exercise 7.1

With Extramarks, students have access to the best teachers and comprehensive courses at an affordable price. Students can find reliable and authentic study materials, like NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 at Extramarks. Sometimes, due to a lack of time, students are not able to cover the entire syllabus, causing them to miss some important topics. Extramarks covers the entire syllabus to ensure that students do not miss any topics and score good marks. Additionally, Extramarks offers curriculum mapping to eliminate the need for students to seek assistance elsewhere. Through the Extramarks website, students can keep track of their preparation levels through learning modules such as In-depth Performance Reports to track progress. As a result of Extramarks, students are able to get a great deal of help building their core fundamentals in order to be able to answer any question in their examinations without any trouble.

Chapter wise NCERT Solutions for Class 9 Maths

The Extramarks website provides young learners with the Class 9 Maths Chapter 7 Exercise 7.1, that are curated by its in-house expert educators. These solutions provide step-by-step, detailed instructions for each and every question. To ensure that students have strong and clear concepts of Class 9 Maths Exercise 7.1, Extramarks walks them through the logic behind each step of the problems in the exercise. It is easy to download the Class 9 Maths Triangles Exercise 7.1 from the Extramarks website. The NCERT curriculum must be on the tips of the students in Class 9. They learn basic concepts of the subject through the NCERT Curriculum. The chapter entitled Triangles of Class 9 Mathematics can be one of the most scoring chapters in the Class 9 final examinations. Since the NCERT books are written by subject experts, students can understand all the concepts of every exercise if they thoroughly go through the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1. Extramarks provides these solutions to help students improve their problem-solving skills and prepare for the examination. All the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, are explained step by step with all the details so that the students do not get confused. It is recommended that learners thoroughly review these solutions prior to their board examinations.

Class 9 Maths Chapter 7 Includes:

Students can achieve success in their examinations with Extramarks’ NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1. Every topic which can appear in the examination is covered in the NCERT textbook. In addition, NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 are compiled by professionals with extensive experience. They are also a very helpful tool for students who find Mathematics challenging since they help them understand the basics of the chapter. Practising the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 helps students with a steady pace for solving the problems related to the curriculum, which is very critical for them to score well in the examinations. Once students go through the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, they will be able to solve any complicated problem that they can encounter in their examinations. Extramarks recommends learners practice the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 thoroughly prior to their examinations.

NCERT Solutions for Class 9

The subject of mathematics can be very intimidating for many students. The first and foremost step that learners must take for the preparation of their Class 9 Mathematics examination is to thoroughly practice the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1. There are, however, no solutions to the questions in the NCERT textbooks.

Therefore, Extramarks provides students with the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 to help them prepare well for their examinations. Through the Extramarks website, students can find NCERT solutions, in which each step of every problem is explained properly along with the summary of the chapter. Practising the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, help students solve problems related to the chapter accurately and at a better pace. As a result, they are able to perform better in their examinations. Students can easily access the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, on the Extramarks website.

CBSE Study Materials for Class 9

Practising the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, is one of the best ways to improve the calculation skills and logical reasoning of students. In addition to constructing strong foundations for the curriculum, these solutions also assist students in applying those concepts practically. The NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, are designed for students to improve their conceptual clarity and mathematical skills efficiently. By going through these solutions, students can practice the concepts and functions of the chapter, which are very essential to succeeding in their examinations. Reviewing the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, is the most important step that students should take in preparation for their examinations.

CBSE Study Materials

Students need plenty of practice in Mathematics to improve their conceptual clarity. The NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 are considered to be one of the best resources for the preparation of the examinations. With their assistance, students are able to solve problems faster and more effectively. The NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, are easily accessible on any device as they are available in PDF format.

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Q.1

$\begin{array}{l} In quadrilateral ACBD, AC = AD and AB bisects ∠ A \\ (see figure below) . Show that ΔABC ≅ ΔABD . What can \\ you say about BC and BD . \end{array}$

Ans

$\begin{array}{l} Given : ABCD is a quadrilateral, AC = BD, AB bisects ∠ A. \\ To prove: Δ ABC ≅ Δ ABD \\ Proof:In Δ ABC and Δ ABD \\ AC = AD [Given] \\ ∠ BAC = ∠ ABD [Given] \\ AB = AB [Common] \\ ∴ Δ ABC ≅ Δ ABD [By SAS] \\ BC = BD [By CPCT] \end{array}$

Q.2

$\begin{array}{l} ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA \\ (see figure below) . Prove that \\ (i) ΔABD ≅ ΔBAC \\ (ii) BD = AC \\ (iii) ∠ ABD = ∠ BAC . \end{array}$

Ans

$\begin{array}{l} Given : ABCD is a quadrilateral, AD = BC, ∠ D AB = ∠ C BA . \\ To prove: \\ (i) Δ ABD ≅ Δ B AC \\ (i i) B D = A C \\ (i i i) ∠ ABD = ∠ BAC \\ Proof: (i) In Δ ABD and Δ B AC \\ AB = B A [Common] \\ ∠ B A D = ∠ A B C [Given] \\ A D = B C [Given] \\ ∴ Δ ABD ≅ Δ BAC [B y SAS] \\ (i i) B D = A C [B y CPCT] \\ (i i i) ∠ ABD = ∠ BAC [B y CPCT] \end{array}$

Q.3 AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

Ans

$\begin{array}{l} Given : AD and BC are equal perpendiculars to a line segment AB. \\ To Prove: CD bisects AB i.e., CO = OD \\ Proof : In ΔBOC ≅ ΔAOD \\ ∠ CBO = ∠ DAO [Given] \\ ∠ BOC = ∠ AOD [Vertical opposite angles] \\ BC = AD [Given] \\ ∴ ΔBOC ≅ ΔAOD [By AAS] \\ ∴ BO = OA [By C.P.C.T.] \\ \Rightarrow CD bisects line segment AB. \end{array}$

Q.4

$\begin{array}{l} l and m are two parallell ines intersected by another pair of \\ parallel lines p and q (see figure below) . Show that Δ ABC ≅ ΔCDA . \end{array}$

Ans

$\begin{array}{l} Given : line l and m are parallel and \overset{⇀}{p} ∥ \overset{⇀}{q} . \\ To prove: Δ ABC ≅ ΔCDA \\ Proof: In Δ ABCand ΔCDA \\ ∠ BAC = ∠ DCA [Alternate interior angles] \\ AC = CA [Common] \\ ∠ BCA = ∠ DAC [Alternate interior angles] \\ Δ ABC ≅ ΔCDA [By ASA] \end{array}$

Q.5

$\begin{array}{l} Line l is the bisector of an angle ∠A and ∠B is any point on l. \\ BP and BQ are perpendiculars from B to the arms of ∠A \\ (see figure below) . Show that : \\ (i) ΔAPB ≅ ΔAQB \\ (ii) BP = BQ or B is equidistant from the arms of ∠ A . \end{array}$

Ans

$\begin{array}{l} Given : Line l is bisector of ∠ A, BP and BQ are perpendiculars to \\ the arms of angle. \\ To prove: (i) Δ APB ≅ ΔAQB \\ (ii) BP = BQ or B is equidistant from the arms of∠A. \\ Proof: (i) In Δ ABQ and ΔAPB \\ ∠ BAQ = ∠ BAP [Given] \\ AB = AB [Common] \\ ∠ AQB = ∠ APB [each 90°] \\ Δ ABQ ≅ ΔAPB [By AAS] \\ (ii) BQ = BP [By C.P.C.T.] \\ \Rightarrow BP = BQ \end{array}$

Q.6 In figure below, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

Ans

$\begin{array}{l} Given : In Δ ABC and Δ ADE, AC = AE, AB = AD and ∠ BAD = ∠ EAC \\ To prove:BC=DE \\ Proof: In Δ ABC and ΔADE \\ AB = AD [Given] \\ ∠ BAC = ∠ DAE [∠ BAD + ∠ DAC = ∠ DAC + ∠ EAC] \\ AC = AE [Given] \\ Δ ABC ≅ ΔADE [By SAS] \\ BC = DE [By C.P.C.T.] \end{array}$

Q.7

$\begin{array}{l} AB is a line segment and P is its mid - point . D and E are \\ points on the same side of AB such that ∠ BAD = ∠ ABE \\ and ∠ EPA = ∠ DPB (see figure below) . Show that \\ (i) ΔDAP ≅ ΔEBP \\ (ii) AD = BE \end{array}$

Ans

$\begin{array}{l} Given : P is mid-point of AB, ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB \\ To prove: (i) ΔDAP ≅ ΔEBP \\ (ii) AD = BE \\ Proof: (i) In Δ DAPand ΔEBP \\ ∠ DPA = ∠ EPB [∠ APE + ∠ EPD = ∠ BPD + ∠ DPE] \\ A P = PB [Given] \\ ∠ DAP = ∠ EBP [Given] \\ Δ DAP ≅ ΔEPB [By SAS] \\ (ii) AD = BE [By C.P.C.T.] \end{array}$

Q.8

$\begin{array}{l} In right triangle ABC, right angled at C, M is the mid - point \\ of hypotenuse AB . C is joined to M and produced to a point \\ D such that DM = CM . Point D is joined to point B \\ (see figure below) . Show that : \\ (i) ΔAMC ≅ ΔBMD \\ (ii) ΔDBC is a right angle . \\ (iii) ΔDBC ≅ ΔACB \\ (iv) CM = \frac{1}{2} AB \end{array}$

Ans

$\begin{array}{l} Given : In right Δ ABC, ∠ C = 90 ° and M is mid-point on \\ hypotenuse AB, CM = DM. \\ To Prove: (i) ΔAMC ≅ ΔBMD \\ (ii) ∠ DBC is a right angle. \\ (iii) ΔDBC ≅ ΔACB \\ (iv) CM = \frac{1}{2} AB \\ Proof : (i) In ΔAMC and ΔBMD \\ AM = BM [Given] \\ ∠ AMC = ∠ BMD [Vertica l opposite angles] \\ CM = DM [Given] \end{array}$

$\begin{array}{l} ∴ ΔAMC ≅ ΔBMD [S . A . S .] \\ AC = DB [By C.P.C.T.] \end{array}$

$\begin{array}{l} (ii) ∠ ACM = ∠ BDM [By C.P.C.T.] \\ \Rightarrow ∠ ACD = ∠ BDC \\ \Rightarrow AC ∥ DB [Alternate angles are equal.] \\ ∠ ACB + ∠ DBC = 180 ° [Co-interior angles] \\ 90 ° + ∠ DBC = 180 ° \\ ∠ DBC = 180 ° - 90 ° \\ = 90 ° \\ So, ∠ DBC is a right angle. \\ (iii) In Δ DCB and ΔACB \\ DB = AC [Proved] \\ ∠ ACB = ∠ DBC [Each 90°] \\ BC = BC [Common] \\ ∴ Δ DCB ≅ ΔACB [S . A . S .] \\ (iv) DC = AB [By C.P.C.T.] \\ 2 CM = AB [CM = DM] \\ CM = \frac{1}{2} AB \end{array}$

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FAQs (Frequently Asked Questions)

1. Are the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 available on the Extramarks website?

Yes, the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 are easily available on the Extramarks website. As these solutions are available in PDF format, they can be easily downloaded on any device, they are curated by the Extramarks subject experts. Along with the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1, Extramarks also provides students with various learning modules that help them with an enjoyable and systematic learning process. Extramarks has proved to the students that e-learning is extremely beneficial. Students can subscribe to the Extramarks website for access to authentic and credible NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1.

2. Is Class 9 Chapter 7 Triangles difficult?

No, Chapter 7 Triangles is not difficult or complicated for the students of Class 9. If they review the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 thoroughly, they will be able to grasp the concepts of the chapter easily and apply those concepts to any complicated problem that can appear in the examinations.

3. Is it essential to practice all the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1?

Yes, students should practice all the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 as every question helps them in building strong concepts. Furthermore, by practising them, students will be able to increase their speed and accuracy, which will help them avoid small calculation errors so that they may not lose marks during examinations.

4. How can students clear their doubts about the NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1?

The NCERT Solutions For Class 9 Maths Chapter 7 Exercise 7.1 provided by the Extramarks website are incorporated in a step-by-step approach and properly detailed so that students can understand the concepts easily. Students can subscribe to the Extramarks website for access to various other reliable study materials. Multiple learning modules are available on the website to help students learn, practice, and excel in their studies. Students can clear their doubts and track their academic progress with learning modules such as Live-Doubt Solving Sessions, Learn Practice Tests, In-depth Performance Reports and much more.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.1

NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.1 Triangles

Access NCERT Answers for Class-9 Maths Chapter 7 – Triangles

NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.1) Exercise 7.1