NCERT Solutions Class 7 Maths Chapter 6

 NCERT Solutions for Class 7 Mathematics Chapter 6 The Triangle and its Properties

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties

You may have learned about triangles in your earlier classes while learning about the different types of geometric shapes. In Chapter 6 Maths Class 7 you’ll be able to develop a better understanding of its core concept:  A triangle, its- types,  angles, sides, and its properties in more detail. NCERT Solutions of Class 7th Mathematics Chapter 6 offers you solutions to the textbook questions that will act as a reference guide while you solve the exercise questions of the chapters.

NCERT Solutions for Class 7 Mathematics Chapter 6 The Triangle and Its Properties – 

Access NCERT Solutions for Class 7 Mathematics Chapter 6– The Triangle and its Properties

Chapter 6 – The Triangle and its Properties Exercises
Exercise 6.1 Questions & Solutions
Exercise 6.2 Questions & Solutions
Exercise 6.3 Questions & Solutions
Exercise 6.4 Questions & Solutions
Exercise 6.5 Questions & Solutions

NCERT Solutions for Class 7 Mathematics Chapter 6 

Go through the following concepts before referring to the solutions of NCERT Class 7 Mathematics Chapter 6. It will help you in understanding the solutions better: 

  1. A median of a triangle is a line segment drawn from a vertex of a triangle to the midpoint of the opposite side. A triangle can, thus, have three medians in all.
  2. An altitude of a triangle is a perpendicular line drawn from a vertex of a triangle to the opposite side. In simpler words, a triangle can have three altitudes in total, just like the median.
  3. The sum of the interior angles of a triangle is always equal to its opposite exterior angle.  
  4. Rule of angle sum property of a triangle: The sum of all the angles of a triangle is always equal to 180°.

NCERT Solutions for Class 7 Mathematics Chapter 6

Chapter 6 of Mathematics NCERT Class 7 covers the following topics:

UNIT TOPIC
6.1 Introduction
6.2 Medians of a Triangle
6.3 Altitudes of a Triangle 
6.4 Exterior Angle of a Triangle and Its Properties
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 Angle Triangle and Pythagoras Property 

6.1 Introduction

A triangle is a closed curve formed by the intersection of three line segments. The line segments are called sides, and the points of intersections are called the vertices while the angles formed at the vertices are known as the angles of the triangle. So, in a triangle, we can say that there are three sides, vertices and angles. . 

Based on sides, the classification of triangles is of the following types: 

  1.  Equilateral triangle- A triangle in which all three sides are equal. 
  2. Isosceles triangle- A triangle in which only  two sides are equal.
  3. Scalene triangle- A triangle in which no two sides are equal.

Based on the angles, the classification of triangles is of the following types: 

  1. Acute angled triangle- Any triangle in which all three interior angles of the triangle are less than 90°. 
  2. Obtuse angled triangle- Any triangle with one of the interior angles of the triangle is more than 90°. 
  3. Right-angled triangle- A triangle in which one of the interior angles of the triangle is 90°. 

6.2 Medians of Triangle

This section deals with a line segment joining a vertex of a triangle to the midpoint of its opposite side, which is called a median. It bisects the opposite side of the triangle into two equal parts and further divides the triangle into two, the two of them having the same area.

6.3 Altitudes of a Triangle

This section deals with an altitude of a triangle which is a perpendicular line segment drawn from the vertex of the triangle to its opposite side. When meeting the opposite side, it makes an angle of 90°. A triangle has three altitudes and the point of intersection of all the three is known as the orthocenter.

6.4 Exterior Angle of a Triangle and its Property

 According to this law the exterior angle of a triangle is always equal to the sum of its opposite interior angles as this is a property of every exterior angle concerning a triangle. 

6.5 Angle Sum Property of a Triangle

In this section, students need to learn yet another important property of a triangle called the angle sum property. It states that the sum of all three angles is always equal to 180°. To prove this, the students can refer to the NCERT Solutions Class 7 Mathematics Chapter 6 and understand how it  can  be proved by using the exterior angle property rule. 

6.6 Two Special Triangles- Equilateral and Isosceles

This section helps the students get a detailed understanding of the different types of triangles based on sides, with a prime focus on Equilateral (all sides equal implying all angles of the triangle are also equal) and Isosceles triangle (any two sides equal implying two angles of the triangle also equal).

6.7 Sum of the Lengths of Two Sides of Triangle

This section explains  how the length of any two sides of  a triangle is always greater  than the length of its third side. To understand the concept clearer, students can refer to the NCERT Solutions Class 7 Mathematics Chapter 6 where this rule is proven and solved through many illustrations. 

6.8 Right Angle Triangle and Pythagoras Property

A right-angle triangle is the one in which at least one angle of the triangle is 90°. Such triangles have a special property which is called the Pythagoras property or Pythagoras theorem. As per this property, the area of a triangle whose one side is a slanting line, called hypotenuse (it is the side opposite to the right angle) is always equal to the squares of the sum of the other two sides. From the solutions, students will be able to get a better understanding of this property. 

Key Features of NCERT Solutions for Class 7 Mathematics Chapter 6

The key points regarding the benefits that the students will receive through the solutions provided on this official website of Extramarks are:

  • Our NCERT Solutions will provide you with a better understanding of all the topics in this chapter. 
  • It will enrich the young learners  as the solutions are easily available  and can be accessed anywhere, anytime as per your schedule and convenience. 
  • It will explain everything in a simple language,  so that the maximum number of students can benefit from it.  

NCERT Solutions for Class 7 Mathematics

NCERT Solutions for Class 7

 The NCERT Solutions helps students in developing a better understanding of the complicated topics . It provides you with in-depth comprehension of the course and encourages you to develop deductive reasoning skills to solve the questions. It encourages the students to master the topic and increase their confidence in achieving a higher grade.

The NCERT Solutions of Extramarks for Class 7 cover all the subjects and concepts in a detailed manner. Students are assisted with  up-to-date solutions and studying Mathematics  couldn’t have  been easier.  So in case you are interested in looking for the solutions for all the subjects of Class 7, you can click on the link given below. 

NCERT Solutions Class 7 Maths Chapter-wise List

Chapter 1 – Integers
Chapter 2 – Fractions and Decimals
Chapter 3 – Data Handling
Chapter 4 – Simple Equations
Chapter 5 – Lines and Angles
Chapter 6 – The Triangle and Its Properties
Chapter 7 – Congruence of Triangles
Chapter 8 – Comparing Quantities
Chapter 9 – Rational Numbers
Chapter 10 – Practical Geometry
Chapter 11 – Perimeter and Area
Chapter 12 – Algebraic Expressions
Chapter 13 – Exponents and Powers
Chapter 14 – Symmetry
Chapter 15 – Visualising Solid Shapes

FAQs (Frequently Asked Questions)

Mathematics is a subject that is always feared by a lot of students. This could be because a lot of them are unable to develop  interest in Mathematics due to the lack of proper guidance. Moreover, it’s a vast subject and  new topics are added every year.  It requires conceptual clarity and regular practice. Being unable to understand its core concepts properly,  students dislike or avoid Mathematics. Thus, the best way to overcome this fear is to identify your problem, take the required assistance from Extramarks solution to overcome it. Clarifying your doubts and practising in- text and end-text exercises thoroughly will surely encourage you to be better at Mathematics. 

Our NCERT Solutions of Mathematics for all classes are one of the most essential study guides. Extramarks subject matter experts  have framed it with the utmost care to make sure your exam preparation isn’t difficult anymore, in fact it’s fun and easy.

Following are some key points to remember while solving exercise questions:

  • Sum of all interior angles of a triangle is 180°.
  • Kinds of angles including alternate, vertically opposite, adjacent and corresponding angles.
  • Sum of two angles lying on the same plane.
  • Angles based on degrees are of three kinds- acute, obtuse and right-angle.
  • Parallel lines and transversal in a triangle.
  • Properties of interior and exterior angles of a triangle.
  • Sum of vertically opposite angles in a triangle.

To score full marks in any topic of Mathematics, revision and practice is the key. Practice will not only help in understanding all the concepts of Chapter 6  at a deeper level, but it will also help you avoid silly mistakes while solving related problems. The more you practice , the easier it gets. Practice day in and day out, to experience exceptional results over time.

A triangle is a closed curve made by the intersection of three line segments. The line segments are called sides, and the points of intersections are called the vertices. The angles formed at the vertices are called the angles of the triangle. Whereas a triangular region includes the interior of the triangle along with the triangle itself.

There is no hard and fast rule. However, it’s good to make a habit of first going through all the examples in the chapter and then solve the unsolved questions. The more you practice, it will be easier for you to grasp all the concepts of this chapter. And in case you fail to understand any of the concepts or problems, the solutions offered by Extramarks for NCERT solutions Class 7 Mathematics will come handy. You  won’t require any other assistance once you begin using solutions and it will save time for other subjects as well.

Based on sides, the classification of triangles is of the following types: 

  •  Equilateral triangle- A triangle in which all three sides are equal. 
  • Isosceles triangle- A triangle in which  any two sides are equal.
  • Scalene triangle- A triangle in which no two sides are equal.

Based on the angles, the classification of triangles is of the following types: 

  • Acute angled triangle- Any triangle in which all three interior angles of the triangle are less than 90°. 
  • Obtuse angled triangle- Any triangle with one of the interior angles of the triangle is more than 90°. 
  • Right-angled triangle- A triangle in which one of the interior angles of the triangle is 90°.