# RS Aggarwal Class 9 Chapter 9 Solutions (Congruence of Triangles and Inequalities in a Triangle)

RS Aggarwal Solutions for Class 9 Maths Chapter 9- Congruence of Triangles and Inequalities will provide you step by step solutions that are going to benefit you for getting highest marks in CBSE exams. In this chapter of RS Aggarwal Class 9 Maths Solutions, there are a total of 43 problems divided into 2 exercises. You will get an idea of different concepts and Problems based on congruent triangles and relations in the set of all triangles. Some of the concepts which can be defined in this chapter are SAS, ASA, AAS, SSS and RHS congruence criterion and inequalities in a triangle together with theorems.

The main purpose of providing you with this solution is to boost your confidence and analyze the weakest areas which require more practice for exams. You can use RS Aggarwal Solutions to solve textbook problems with less difficulty in less time.

Instasolv’s RS Aggarwal Solutions for chapter 9- Congruence of Triangles and Inequalities in a triangle help clear their basic understanding regarding this chapter as there is a probability of higher marks questions from this chapter. Solving the exercise wise problems daily helps students improve their problem solving and logical thinking skills, important to obtain a better academic score.

## Important Topics for RS Aggarwal Solutions for Class 9 Maths Chapter 9 – Congruence of Triangles and Inequalities in a Triangle

- This chapter will help you to understand the basic concepts of congruent triangles: They are triangles that have equal size and shape. This way, the corresponding aspects are equal and the corresponding angles are the same.

- In this lesson, we will keep in mind the 4 guidelines to show triangle congruence. They are known as the SSS rule, SAS rule, ASA rule, and AAS rule.
- The SSS rule states that: side –side -side

If three sides of 1 triangle are identical to three aspects of some other triangle, then the triangles are congruent.

In the diagrams below, if AB = RP, BC = PQ, and CA = QR, then triangle ABC is congruent to triangle RPQ.

**The SAS rule states: side –angle -side**

- If 2 sides and 1 angle of a triangle are the same at both sides and include the angle of another triangle, then the triangles are congruent.

The *included angle* is said to be an angle formed by 2 given sides.

*For 2 triangles below, if AC = PQ, BC = PR and angle C = angle P, then by using the SAS rule, triangle ABC is always congruent to triangle QRP*

The AAS rule states: angle –angle -side

- If any 2 angles along with a non-included side of a triangle are equal to 2 angles and another non-included side of another triangle, then the triangles are said to be congruent.
- In these diagrams, assume if
*AC*=*QP*, angle*A =*angle*Q*, and angle*B =*angle*R,*then the triangle*ABC*is congruent to triangle*QRP*.

**Three ways to prove triangles congruent**:

Lesson on SAS, ASA, and SSS.

1.**SSS Postulate**: If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding aspects of the alternative triangle, the 2 triangles are congruent.

2.**SAS Postulate**: If there exists a correspondence among the vertices of triangles such that the two sides and the covered angle of one triangle are congruent to the corresponding elements of the other triangle, the 2 triangles are congruent.

3.**ASA Postulate**: If there exists a correspondence between the vertices of two triangles such that angles and the blanketed side of one triangle are congruent to the corresponding components of the other triangle, the 2 triangles are congruent.

### Exercise Discussion of Important Topics of RS Aggarwal Solutions for Class 9n Chapter 9- Congruence of Triangles and Inequalities in a triangle

- The first exercise 9A of Chapter 9 essentially contains 27 questions that will ask you to solve problems related to SAS, ASA, AAS, SSS and RHS congruence criterion and inequalities in a triangle along with theorems with the help of diagrams given respectively.
- The second exercise 9B of Chapter 9 will give reason type problems having 16 questions that will ask you to justify your answers that are mainly based on isosceles triangles, angles of longest sides of triangles and quadrilateral sides of a triangle.
- Math Chapter 9 Exercise contains several problems with solutions that are marked fetching in nature.
- Instasolv will help you in solving and clarifying your doubts about the questions in this Exercise. Even though these exercises seem very simple, they need good preparation.
- Instasolv RS Aggarwal Maths solutions for class 9, Chapter 9 will help you to revise the whole chapter in less time. Any question related to these exercises that you find while solving a problem can be solved immediately. The solution is being developed in stages, making it easier to understand concepts.

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