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

NCERT Solutions for Class 7 Maths Chapter 6 is all about triangles. In this chapter, there are a total of 5 exercises and 21 questions. The Chapter covers triangles in detail including its medians, altitudes, exterior angles, isosceles and equilateral triangles, right-angled triangles and the Pythagoras theorem.

NCERT Solutions for Class 7 Chapter 6 ‘The Triangle and Its Properties’ is based on the latest CBSE approved syllabus. At Instasolv, we provide the most reliable study material for Class 7 Maths. Chapter-wise Solutions of NCERT Class 7 Maths Book are provided that help you in understanding the concepts to score higher marks in the exams.

Triangles are a very important part of geometry and a complete domain called trigonometry is there for those pursuing higher studies in this domain. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. The same sequence of the textbook is followed so that it becomes easy to understand and use as a reference.

## NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and Its Properties: Exercise Discussion

The  Exercises of CBSE Class 7 Maths Chapter 6 is based on the topics discussed below. We would recommend you to understand the topics given below in order to get a good hold of the chapter – The Triangle and Its Properties. There are a total of 5 exercises carrying 21 questions.

1.  Introduction – A triangle can also be called a simple closed curve made of three line segments. A triangle has three angles, three vertices, and three sides.
2. Medians of a Triangle – The line segment joining the midpoint of a side to its opposite vertex is called the median of a triangle. There are three sides and three vertices in a triangle so there will be three medians of a triangle.
3. Altitudes of a Triangle – The perpendicular line segment with one point starting from any side of a triangle and ending at the opposite vertex is called the altitude of the triangle. As in medians, there are three altitudes of a triangle. The altitude is also referred to as the height of the triangle.
4. Exterior Angle of a Triangle and its Property

Extend any side of a triangle. The angle formed at the vertex from where the side has been extended is called an exterior angle of the triangle. Out of the three interior angles of a triangle, one will be adjacent to the exterior angle and two interior angles will be opposite to the exterior angle.

An exterior angle of a triangle is equal to the sum of its interior opposite angles. This relation between an exterior angle and its two interior opposite angles is referred to as the exterior angle property of a triangle.

1. Angle Sum Property of a Triangle

The total measure of all three interior angles of a triangle is always equal to one hundred and eighty degrees.

1. Two Special Triangles: Equilateral and Isosceles

Equilateral Triangle: When all three sides of a triangle are equal it is called an equilateral triangle.

All the three interior angles of an equilateral triangle are equal in measure. Since the total of all interior angles of any triangle is one hundred and eighty degrees, each interior angle of an equilateral triangle is sixty degrees.

Isosceles Triangle: When any two sides of a triangle are equal in length, it is called an isosceles triangle.

The base angles opposite to the equal sides are equal in measure.

1. Sum of the Lengths of Two Sides of a Triangle

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

This also means that the difference in the length of any two sides of a triangle is smaller than the length of the third side of the triangle.

1. Right Angled Triangles and Pythagoras Property

The side of the right-angled triangle which is opposite to the right angle is called the hypotenuse. The sides containing the right angle between them are called the legs of the right-angled triangle.

Pythagoras was a Greek philosopher of the sixth century B.C. He found this useful property which is now known as the Pythagoras theorem. According to his theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Alternatively, if this Pythagoras property holds in any triangle then that triangle must be right-angled.

This is an important property with several practical applications and will be used in maths quite frequently.

## Study Tips for NCERT Class 7 Maths Chapter 6 ‘The Triangle and Its Properties’

Every student has an aim to get a high score in the exams. Instasolv recommends that you read chapter 6 The Triangle and Its Properties of CBSE NCERT textbook for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. Use this summary as a ready reference. It will also help in improving your conceptual clarity.

The Pythagoras property which is the last part of this chapter must be understood and practiced well. This is a widely used concept in practical applications and your later studies. You should expect questions on it and Instasolv recommends that you practice this part very well.

1. If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support.
2. Do all the exercises, solved examples and self-practice questions on your own before you cross-check from the NCERT Solutions for Class 7 Maths or ask the experts on the Instasolv app.