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NCERT Solutions for Class 9 Maths Chapter 7 – Triangles

NCERT Solutions for Class 9 Maths Chapter 7 will help you in learning how to solve Math problems that use the criteria for the Congruence of Triangles. In these exercise of NCERT Solutions, you will also learn about the properties of triangles and theorem of inequalities in triangles in addition to the revision of congruence rules that you studied in your previous classes such as side-side-side (SSS), angle-side-angle (ASA), side-angle-side (SAS), and RHS congruence rule. This is a conceptual chapter and might turn out to be the most scoring one if you are able to grasp the theorems correctly.

There are 31 problems in 5 exercise-sets including an optional exercise with 4 advanced-level questions in the CBSE NCERT Class 9 Maths Chapter 7. These questions will help you revise all the theorems and their applications in a profound manner. The NCERT exercise solutions will help you approach your exam with a downright attitude. The NCERT questions are of varying difficulty level with hints given for the most complicated conceptual ones. You will also find some questions in the form of theorems that you can use in the latter part of the exercise questions.

Instasolv has made sure that our Maths NCERT Solutions for Class 9 Chapter 7 become a one-stop destination for all your queries in the Chapter. Our NCERT Maths Solutions are prepared by professionals to assist you with the simplest yet most sophisticated answers. They are an apt resource for an in-depth study as well as a quick revision for your CBSE exam. Take a look at the Summary of Chapter 7 given below and revise all the important topics before you solve the NCERT problems. 

Important Points of NCERT Solutions for Class 9 Maths Chapter 7

Introduction:

  1. Congruent figures are the ones that have equal shapes and sizes or are equal in all respect.
  2. There are numerous examples in which congruence of triangles is used in daily life situations, such as whenever identical objects have to be made, the casts have to be congruent.
  3. Two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
  4. Therefore in congruent triangles, corresponding parts are equal and we use the abbreviation CPCT for corresponding parts of corresponding triangles.
  5. A triangle in which any two sides are equal is known as an isosceles triangle.

SAS Congruence Rule:

If in two triangles, the triangles have the corresponding pairs of two sides and the included angles between them equal, then the two triangles are congruent.

Note: SAS congruence rule is correct but not ASS or SSA rule.

ASA Congruence Rule:

If in two triangles, the triangles have the corresponding pairs of two angles and the included side between them equal, then the two triangles are said to be congruent.

Also, the AAS Congruence rule is correct if two pairs of angles and any one pair of corresponding sides, in the given two triangles are equal.

SSS Congruence Rule:

Two triangles will be congruent if all the sides of one triangle are equal to all the corresponding sides of another triangle by the SSS Congruence rule. This theorem can be proved by combining the above results.

RHS Congruence Rule:

If the hypotenuse and one side of one right triangle turn out to be equal to the hypotenuse and one side of another triangle, then the given two right-angled triangles are said to be congruent. RHS is an abbreviation for Right Angle, hypotenuse and side.

Inequalities in a Triangle:

  1. There is a relation between the unequal sides and unequal angles of a triangle.
  2. The larger side has a greater angle opposite to it than the smaller side in a triangle.
  3. The larger angle has a larger side opposite to it, in general in all the triangles.
  4. The sum of any two sides of a triangle will always be greater than the length of the third side.

Highlights of CBSE Class 9 NCERT Maths Chapter 9: Triangles

  • The corresponding sides of congruent triangles are equal.
  • Triangles can be congruent by various criteria such as ASA rule, SAS rule, SSS rule and RHS rule.
  • Equal sides have equal opposite angles in a triangle and equal angles have equal opposite sides in a triangle.
  • The sum of any two sides is greater than the third side.

Discussion of Exercises of NCERT Solutions for Class 9 Maths Chapter 7

  1. The NCERT exercises for Class 9 Maths Chapter 7 are based on the Axioms and Theorems of Triangles and Congruence of Triangles discussed in the Chapter. 
  2. For solving Exercise 7.1, you need to have a thorough understanding of the SAS Criteria of Congruence.
  3. For solving Exercise 7.2, you need to have a thorough understanding of the basic theorems of Triangles angle bisectors, angle sum property etc. 
  4. The questions of Exercise 7.3 are subjective and will boost your analytical skills. You must have a clear idea of types of triangles and their properties then only you will be able to solve the questions of this exercise. 
  5. The questions in Exercise 7.4 involve theorems relating to the inequality principles of the triangles.
  6. Exercise 7.5 is optional. It employs all the axioms and theorems studied by you in the chapter for a comprehensive understanding of the Chapter.

Benefits of NCERT Class 9 Maths Chapter 7 Solutions Provided by Instasolv

  • Instasolv makes sure you grasp the important theorems of the NCERT Solutions for Class 9 Maths Chapter 7.
  • You will find all the NCERT answers adhering to the instructions provided by CBSE, therefore you can solve the questions in the same way in your CBSE exams.
  • There is no doubt that our exercise-wise NCERT Solutions for Class 9 Maths Chapter 7 will make it easier for you to score well
  • All the exercise questions are covered including the optional exercise questions as well.