# NCERT Exemplar Class 9 Maths Chapter 7 Solutions: Triangles

NCERT Exemplar Class 9 Maths Solutions for Chapter 7 are going to give you detailed knowledge about triangles. This chapter of NCERT Class 9 Maths Exemplar consists of around 25 questions in total covering 4 exercises. The exercises cover questions on different topics like congruent figures, triangles, its types, some criterion for the congruence of triangles, etc. One of the very important concepts of this chapter is the theorems related to inequalities of triangles.

The Exemplar problems of the chapter are based on the latest CBSE exam pattern. They can help you build a strong understanding of all the concepts of the chapter. So, practising NCERT Exemplar will be a good choice on your end. The exercises contain all levels of questions that will help in preparing the best for the exams. It will also help you in various inter-school and national level olympiads.

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## Important Topics for NCERT Exemplar Class 9 Maths Solutions Chapter 7: Triangles

**Congruent figures**

Geometrical figures that have the same size, as well as shape, are known as congruent. In order to verify if plain figures are congruent or not, you can place them on one another and you can check if they match.

**Triangle **

Any closed figure that consists of three sides is known as a triangle. It consists of three sides, three angles as well as three vertices.

**Types of Triangles**

There are around three types of triangles that are based on the length of the sides.

- Scalene Triangle: The length of all sides of the scalene triangle is different.
- Isosceles Triangle:
**this triangle has two equal sides.** - Equilateral Triangle: A triangle that has three equal sides is known as the equilateral triangle.

**Types of Triangle on the Basis of Angles**

- Acute Triangle
**: A triangle in which the three angles are less than 90 degrees.** - Obtuse Triangle: A triangle in which one angle is greater than 90 degrees.
- Right Triangle: A triangle in which one of the angles is 90 degrees.

**Congruent figures**

Geometrical figures that have the same size, as well as shape, are known as congruent. In order to verify if plain figures are congruent or not, you can place them on one another and you can check if they match.

- Any two circles are known to be congruent if they have the same radius.
- Any two squares are known to be congruent if they have equal sides.

**Congruent Triangle**

A triangle is congruent if its corresponding angles, as well as sides, are equal.

**Criteria for Congruence of Triangles**

The different criteria for the congruent angles are:

- SAS (side-angle-side) congruence rule
- ASA (angle-side-angle) congruence rule
- AAS (angle-angle-side) congruence rule
- SSS (side-side-side) congruence rule
- RHS (right angle-hypotenuse-side) congruence rule

In the chapter, you will study in detail about all of the above mentioned, congruence rules.

### Exercise Discussion of NCERT Exemplar Class 9 Chapter 7 Triangles

- Exercise 7.1 consists of 5 questions that test your skills if you can choose the correct answer from the given question. This exercise checks if you have an understanding of the topics like congruence of triangles, finding the angle given other sides or things, etc.
- Exercise 7.2 has 6 questions that test your reasoning skills on different topics of the chapter like giving justification to the question if the triangle meets the congruency rules, or how to construct a triangle given its sides and one of the angles, etc.
- Exercise 7.3 has 5 questions in which you need to prove the different situations asked in the question. You will have to show if the sides are equal given isosceles triangle, showing if the triangles are congruent, etc.
- Exercise 7.4 asks you to find the angles or prove the situation given in the question. This exercise consists of around 10 questions. You are required to find angles of the triangle, proving different angles equal, etc.
- NCERT Exemplar has the exercises that cover all the topics of the chapter and tests your basic understanding regarding the chapter.

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