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NCERT Solutions for Class 9 Maths Chapter 7 Triangles

The NCERT Solutions for Class 9 Maths Chapter 7 Triangles will make you understand all the important concepts like congruence and inequalities of triangles. Congruent means equal in all respects. Congruent triangles are equal in shape and size. For example, if you place two circles of the same radius over each other, they will completely cover each other and hence are called congruent circles. For triangles, you will study how to determine the corresponding parts of congruent triangles. You will learn the SAS, ASA, SSS, RHS, and other congruent rules in these solutions. 

Our NCERT Solutions for Class 9 Maths Chapter 7 also include question-answers related to inequalities of triangles where you will study some important theorems related to triangles. These NCERT solutions are created by the askIITians team of Maths experts who have years of experience in teaching Class 7 Maths concepts to the students. All the solutions are based on the latest syllabus and exam pattern to help you prepare for your examination easily. You can download these solutions right away and get started. 

About NCERT Solutions for Class 9 Maths Chapter 7 Triangles

Before you start working on the NCERT solutions, here are some important concepts of the Triangles chapter that students must know. 

  • SAS Congruence Rule: Two triangles are congruent with each other if their two sides and an angle between those sides are equal to each other.
  • SSS Congruence Rule: Two triangles are congruent with each other if all three sides are equal. 
  • ASA Congruence Rule: Two triangles are congruent with each other if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
  • RHS Congruence Rule: For two right triangles, if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, they are congruent with each other. 
  • The Sum of any two sides of a triangle is greater than the third side. 
  • Angles opposite to equal sides of a triangle are equal. 
  • Sides opposite to equal angles of a triangle are equal. 
  • In a triangle, the angle opposite to the longer side is larger (greater). 
  • In a triangle, the side opposite to the larger (greater) angle is longer.

The NCERT Class 9 Maths Chapter 7 includes 5 exercises and 31 questions in total. All these exercises are important from the exam point of view and students must practice them thoroughly for a better understanding of the concept of congruence and inequality of triangles. Let us see what each exercise of this chapter includes and what is important in this chapter. 

Download NCERT Solutions for Class 9 Maths Chapter 7 Triangles

Chapter 7 Class 9 Maths NCERT questions are quite tricky as they involve the concept of congruence which is relatively new for students. Many students would think that why do we need to learn about congruence or inequalities between triangles anyway. Well, these concepts are quite important for higher studies where students who chose Architecture or Design fields. Some common applications of this chapter include:

  • Construction 
  • Truss Bridge (based on SSS rule)
  • Geodesic Dome  (based on ASS rule)

Download our NCERT Solutions for Class 9 Maths Chapter 7 Triangles exercise-wise from the links given below. 

  • Class 9 Maths Chapter 7 Ex 7.1 Solutions - 8 Questions
  • Class 9 Maths Chapter 7 Ex 7.2 - Solutions 8 Questions
  • Class 9 Maths Chapter 7 Ex 7.3 - Solutions 5 Questions
  • Class 9 Maths Chapter 7 Ex 7.4 - Solutions 6 Questions
  • Class 9 Maths Chapter 7 Ex 7.5 - Solutions 4 Questions

NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.1

The first exercise of this chapter is based on finding whether the given triangles are congruent using the SAS and ASA congruence rules. Study these rules thoroughly before solving this exercise. This exercise is quite simple and questions are directly based on SAS and ASA rules and you do not have to perform any complex calculations in this exercise.  

There are 8 questions in this exercise that are solved step by step in our NCERT solutions. We advise you to read the questions carefully and take note of all the important information given in them. For example, in question 3, you are given a figure where AD and BC are perpendiculars and you have to show that CD bisects AB. Download the NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.1 right away and start solving. 

NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.2 

The second exercise of this chapter is based on some important properties of triangles such as angles opposite to equal sides of an isosceles triangle are equal, the sides opposite to equal angles of a triangle are equal. Using this theorem along with SAS and ASA congruence rules, you have to solve this exercise. For example, in question 2, you are given that AD is the perpendicular bisector of BC in triangle ABC and you have to show that triangle ABC is isosceles with AB=AC. 

There are 8 questions in this exercise and all of them are important. You must try to solve them on your own first and if you face any problems our free NCERT solutions for Class 9 Maths Chapter 7 are available for you. The stepwise explanations included in these solutions will make it easy for you to understand the exercise and master it.

NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.3 

The third exercise of Class 9 Maths Chapter 7 is based on SSS and RHS congruence rules. The questions are not straightforward where you just have to prove the congruence of the triangles. But, these questions often include the application of these congruence rules to prove that two sides or two angles are equal. For example, in question 2 you are given that AD is an altitude of an isosceles triangle ABC in which AB = AC. Then, you have to show that AD bisects BC and AD bisects angle A. 

Solving questions where you have to prove something requires step by step solutions. If you miss out on any step, you will lose marks. Learn how to write a solution step by step using our NCERT Solutions for Class 9 Maths Triangles Chapter. All these solutions are completely reliable as they are created by our team of online Maths experts. We make sure that these solutions are self-explanatory. 

NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.4 

You need to learn three important theorems before solving this exercise: 

  1. If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). 
  2. In any triangle, the side opposite to the larger (greater) angle is longer. 
  3. The sum of any two sides of a triangle is greater than the third side.

There are 5 questions in this exercise where you have to apply these theorems and provide the answer. Students often find these questions tricky as they have to apply a theorem and prove the answer. There are no practical calculations involved and most of the solutions are theoretical. But once you master how to solve such questions easily, you can score full marks in this chapter. If you face any problems, our online NCERT solutions are available for you. 

NCERT Solutions for Class 9 Maths Chapter 7 Ex 7.5

The last exercise of this chapter is optional but we recommend you solve it. This will help you brush up on all important points about this chapter and prepare you well for the exam. This exercise includes just 4 questions that will build your fundamental understanding of the chapter. 

The questions of this exercise are of advanced level so you might require some assistance. For that, our free NCERT solutions are available. They are self-explanatory and easy to understand. So, you will not face any problem in completing the NCERT solutions of this chapter successfully. 

Why NCERT Solutions for Class 9 Maths Chapter 7 Triangles are Important? 

Many students find chapters like Triangles difficult as they include more theorems than practical calculations. Students have to apply these theorems in the questions and provide a solution. There is a specific pattern of writing the answers step by step so that you can get full marks. Our NCERT solutions act as a guide for the students and help them understand how to master this chapter for exams. NCERT Solutions for Class 9 Maths Chapter 7 are important because:

  • Easy Understanding of Concepts: These solutions solidify the concepts of congruence and inequality of triangles so that students can achieve full marks in this chapter. 
  • Preparation for Advanced Concepts: In higher classes, you will study concepts based on this chapter so must study all the NCERT problems thoroughly and create a solid foundation. 
  • Self-paced Learning: There is no rush. You can take your time in solving these questions one by one. Just download our free NCERT solutions for reference. 

Download our NCERT Solutions for Class 9 Maths Chapter 7 today and start learning. 

NCERT Solutions for Class 9 Maths Chapter 7 FAQs

  1. How many questions are there in Class 9 Maths Chapter 7?

NCERT Class 9 Maths Chapter 7 Triangles includes 31 questions in total. All these questions are important from the exam perspective. 

  1. What are the important concepts of Class 9 Maths Chapter 7?

Important concepts of Class 9 Maths Chapter 7 Triangles include Congruence of triangles, Criteria for congruence of triangles (SAS congruence rule, ASA congruence rule, SSS congruence rule, RHS congruence rule), Properties of triangles and Inequalities of triangles.

  1. How NCERT solutions will help me in preparing this chapter? 

These NCERT Class 9 Maths Solutions for Chapter 7 are created based on the latest syllabus so include all the updated concepts that will be asked in the exam. Solving the exercise questions of this chapter will increase your confidence and make you more prepared for the examination. You will easily get familiar with the type of questions that can be asked in exams. 

  1. I need additional help in Class 9 Maths, what should I do? 

Don’t worry, the askIITians team is here to help you. Our plethora of free study resources will help you understand Class 9 Maths concepts in a breeze. For example, revision notes, sample papers, and previous year papers. We also provide CBSE online classes for Class 9 Maths where you can study in Live Classes from askIITians experts. 

  1. How to solve the NCERT questions of this chapter? 

You must first understand the concepts included in the chapter and practice the solved examples. Then, solve the NCERT exercises one by one. In case of any confusion, refer to our NCERT Solutions for Class 9 Maths Chapter 7. 


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