# RD Sharma Class 9 Chapter 9 Solutions (Triangles and its Angles)

RD Sharma Class 9 Maths Solutions for Chapter 9** **in order to assist you in solving the exercise questions of triangles and the angles related to them. This is an introductory chapter about triangles. In this chapter, you will get to learn about the types of triangles and some important theorems about triangles and angles related to them. This chapter of RD Sharma Solutions will help you to understand the core concepts in the geometry of triangles. This, in turn, will build a strong foundational base for you to understand the congruence of triangles.

There are 11 questions categorized into 2 exercises in Class 9 RD Sharma Chapter 9. An additional VSAQs exercise is provided consisting of 6 questions in total to help you practice rigorously for your exams. There is an extensive horizontal and vertical coverage of all the topics in this chapter in these exercise questions. By solving these questions thoroughly, you will be able to prepare yourself for the national level scholarship exams. The exercises include mathematical as well as theoretical problems such as verification questions and proof of theorems based on diagrams. Fill in the blanks, true or false, and definition problems are all part of the exercise questions.

We have provided the answers in a simplified format so that you don’t develop doubts over doubts. You will get the answer to each question with 100% accuracy and precision. The answers despite being on-point, have each step explained in detail with adequate reasoning. It is advised that as soon as you stumble upon a question, you should immediately seek reference from the Instasolv platform for appropriate guidance in line with the CBSE trends and guidelines. This will also help you to make the most of your daily maths practice sessions.

## Important Topics for RD Sharma Solutions for Class 9 Chapter 9: Triangle and Its Angles

**Introduction to Triangles**

A closed figure that consists of 3 sides is termed as a triangle. A triangle includes 3 vertices, 3 sides, and 3 angles.

**Types of Triangles**

Triangles can be categorized on either the basis of their angles or on the basis of the length of their sides. These categories are discussed below:

**Types of triangles on the basis of their angles**

- Acute Triangle: In an acute triangle, all the angles of the triangle are less than the right angle.
- Obtuse Triangle: In an obtuse triangle, at least one angle of the triangle is greater than the right angle.
- Right Angled Triangle: In the right-angled triangle, one angle is equal to the right angle. The side opposite to this angle is the longest side and is termed as the hypotenuse. The other two sides are known as the base and the perpendicular.

** Types of triangles on the basis of their sides**

- Scalene Triangle: A scalene triangle is the one with all unequal sides.
- Isosceles Triangle: In such a triangle, two sides are equal.
- Equilateral Triangle: All the sides in an equilateral triangle are equal. All the angles in an equilateral triangle are equal to 60°.

**Angle Sum Property of a Triangle**

The angles of any triangle under consideration totals to give a result of180°.

**Exterior Angle Property of a Triangle**

According to this theorem, you will get to find that the exterior angle of a triangle on an extended side is always equal to the sum of the two opposite interior angles.

We know that vertically opposite angles in two intersecting lines are always equal. The linear pair of angles add up to give a result of 180°.

**Theorem 1**

Angles opposite to equal sides in a triangle are also equal. Therefore, in the isosceles triangle, two angles are also equal.

**Theorem 2**

If in a triangle under consideration, two angles are equal, then the two sides opposite to it will also be equal.

**Theorem 3**

The sum of two sides of a given triangle will always be greater than the third side. If the condition fails to satisfy, the triangle is impossible.

**Theorem 4**

If the area of a triangle equal to zero, then the three points under consideration are collinear, that is, they lie on the same line.

### Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 9: Triangle and Its Angles

- The questions in exercise 9.1 are all based on the angle sum property of the triangles.
- In exercise 9.2, you will get to evaluate the value of angles based on the properties of vertically opposite angles, linear pair of angles, and the exterior angle theorem of triangles.
- The VSAQs exercise questions contain the miscellaneous problems based on theoretical questions on the important theorems of triangles.
- The questions are of diverse nature with respect to the difficulty level of the concepts.

## Benefits of RD Sharma Solutions for Class 9 Chapter 9: Triangle and Its Angles

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