NCERT Solutions for Class 7 Maths, Chapter 6 - The Triangle and Its Properties

The NCERT Class 7 Maths, Chapter 6, deals with Triangles and its Properties.  In this chapter, you will learn what triangles are, types of triangles and their properties in detail, which will help you to solve problems related to the triangle. A triangle is formed when three line segments meet to make a closed figure. There are three angles in a triangle. In this chapter, you will learn about the special characteristics of triangles that will also be useful to you in the Higher classes. Learning the properties of a triangle well, helps you to understand all the further concepts better. This chapter also highlights the Pythagorean Theorem, which is one of the most important theorems on Triangle and its Properties.

To know more about this Chapter, let’s look at the topics and sub-topics of this Chapter:

6.1 Introduction

6.2 Medians of a Triangle

6.3 Altitudes of a Triangle

6.4 Exterior Angle of a Triangle and Its Property

6.5 Angle Sum Property of a Triangle

6.6 Two Special Triangles: Equilateral and Isosceles

6.7 Sum of the Lengths of Two Sides of a Triangle

6.8 Right-Angled Triangle and Pythagoras Property

In Class 7 Maths Chapter 6, you will learn-

Section 6.2 – This section deals with the medians of a triangle. It helps one to understand the importance of Medians in a triangle. You can learn how to find the medians in a triangle and also the perpendicular bisector. The line joining the vertex of a Triangle to the mid-point on the opposite side of the triangle is the median. It helps you to find the length of an unknown side of a triangle.

Section 6.3 – This section deals with the altitudes of a triangle. It helps you to measure the height (altitude) of a triangle. Besides, this section also helps you to learn the procedure to measure the height of the Triangle, which can be used to solve other complex problems on Triangles.

Section 6.4 – This section deals with the exterior angle and its property. If any line of the triangle is extended, it forms an exterior angle. In this section, you will learn about the interior opposite angles that are the angles opposite to the exterior angle in a triangle. You will also learn about the main property of exterior angle i.e., the exterior angle of a triangle is the sum of its interior opposite angles.

NCERT Class 7 Maths, Chapter 6 is a chapter exclusively on Triangle and its Properties. You will learn the properties of triangles that might be used as a basis to solve various problems on triangles. The concept of a triangle is a very crucial part of geometry; it helps you to solve various complex problems related to distance, direction and is used in designing products or even in the field of architecture.

Section 6.5 – In this section, you will learn the main property of a triangle i.e., the Angle Sum Property. You will also be taught how and why the sum of all the angles of a triangle is 180 degrees. Several solved examples given in this section of the chapter will help you understand this property in an easy way. This will further make solving problems to find the value of any unknown angle of a triangle considering this Angle Sum Property, easier for you.

Section 6.6 – This section deals with two special triangles: Equilateral and Isosceles Triangle. In this section, you will learn about the aforementioned triangles, their properties such as- in an equilateral triangle, all the three sides are of equal length; whereas in an isosceles triangle, two sides equal. This section helps you to know the difference between equilateral and isosceles triangles.

Section 6.7 – This section deals with the sum of the two sides of a triangle. You will learn that the sum of the two sides of a triangle is always greater than the third side. This is another important property of a triangle. This property is applied to problems when you have to find the length of any unknown side.

Section 6.8 – This section deals with a special kind of triangle called the Right-Angled Triangle. You will also learn about Pythagoras, a Greek Mathematician who found this very important and useful property of Right-Angled Triangle. Besides, you will learn about hypotenuse and the property related to the other two sides of the hypotenuse in this section. You will also learn the property that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This property is very useful and is called Pythagoras Theorem.  Further, you will be able to prove that if any triangle justifies this property, it is considered to be a Right-Angled Triangle.

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