NCERT Solutions for Class 10 Maths Chapter 6 Triangles

 

NCERT Solutions for Class 10 Maths Chapter 6 Triangles help you find out how to solve the exercise questions of this chapter correctly. Many times Class 10 students face difficulty in solving the NCERT questions which affect their board exam preparation. This is why askIITians Maths experts have created stepwise solutions for all the NCERT exercises of Class 10 Maths Chapter 6 Triangles. You can refer to these solutions at any time and solidify your conceptual understanding of the chapter. These solutions are free to download and are available in pdf format. Let us see what is included in the NCERT exercises of Class 10 Maths Chapter 6 Triangles and how our NCERT Solutions for the chapter will benefit you. 

About NCERT Class 10 Maths Chapter 6 Triangles 

 

Chapter 6 Triangles of Class 10 Maths is based on the congruence of figures. You will learn how to find out whether the given triangles are similar or not. This chapter also includes various theorems based on the similarity of triangles and areas of similar triangles. You will also learn about the Pythagorean Theorem. You must revise all the theorems of the chapter before you start solving the NCERT exercises of the chapter. 

 

Important points related to NCERT Class 10 Maths Triangles Chapter 

 

The similarity of Triangles: Two triangles are called similar if: 

1. their corresponding angles are equal
2. their corresponding sides are in the same ratio (or proportion).

Criteria for similarity of triangles: 

• AAA (Angle-Angle-Angle) Similarity Criterion for two triangles: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar. 
   
• AA Similarity Criterion for two triangles: If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
   
• SSS (Side–Side–Side) Similarity Criterion for two triangles: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.
   
• SAS (Side–Angle–Side) Similarity Criterion for two triangles: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. 

Equiangular Triangles: If corresponding angles of two triangles are equal, then they are known as equiangular triangles. The ratio of any two corresponding sides in two equiangular triangles is always the same.

 

Important theorems related to Class 10 Maths Chapter 6 Ex 6.6:

 

• If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and each other.
• Pythagoras Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
• The converse of Pythagoras Theorem: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. 
• Baudhayan Theorem: The diagonal of a rectangle produces by itself the same area as produced by both sides (i.e., length and breadth). 
• Basic Proportionality Theorem (Thales Theorem): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
• The converse of Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
• The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In the given image: 

 

 

If ∆ABC ~ ∆PQR, then 

 

Download Free NCERT Solutions for Class 10 Maths Chapter 6 Triangles 

 

NCERT Chapter 6 Class 10 Maths Ex 6.1 Solutions 

The first exercise of this chapter includes 3 questions. This exercise is based on the introduction to congruence figures and similar figures. All the questions in this exercise are of short answer type. We have provided comprehensive solutions to each question so for your basic understanding. 

 

NCERT Chapter 6 Class 10 Maths Ex 6.2 Solutions 

The second exercise of this chapter includes 10 questions. This exercise is based on the similarity of triangles. It also includes two important theorems of the chapter - the theorem of equiangular triangles and the basic proportionality theorem. You will also study the converse of the basic proportionality theorem. Our stepwise solutions will help you understand how to solve questions of this exercise from the exam's point of view. 

 

NCERT Chapter 6 Class 10 Maths Ex 6.3 Solutions 

The third exercise of this chapter includes 16 questions. This exercise is based on different criteria for similarity of triangles such as AAA (Angle-Angle-Angle), AA, SSS (Side–Side–Side) and SAS (Side–Angle–Side). All the questions of this exercise require proper reasoning. If you have any doubts about this exercise our NCERT Solutions will provide you with complete guidance. 

 

NCERT Chapter 6 Class 10 Maths Ex 6.4 Solutions

The fourth exercise of the Triangles chapter includes 9 questions. This exercise is based on areas of similar triangles. The exercise includes a combination of short answer and long answer type questions. In this exercise as well, you have to provide proper reasoning and explanations. Check our NCERT solutions for this exercise and see whether your answers are correct or not. 

 

NCERT Chapter 6 Class 10 Maths Ex 6.5 Solutions 

The fifth exercise of this chapter includes 17 questions. This exercise is based on the Pythagoras theorem and its converse. In most of the questions of this exercise, you have to prove that the given triangle is a right triangle using the Pythagorean theorem. 

 

NCERT Chapter 6 Class 10 Maths Ex 6.6 Solutions

The last exercise of this chapter includes 10 questions. It is an optional exercise which means that the questions in this exercise are not based on the examination perspective. However, you must practise all the questions of this exercise as it will help you test your knowledge regarding the concepts introduced in this chapter. 

 

Why you must download NCERT Solutions for Class 10 Maths Chapter 6 Triangles from the askIITians website: 

• All the solutions for Chapter 6 Triangles are organised exercise-wise for your easy understanding. 
• We have provided stepwise solutions for every question so that you can understand how to approach such problems in the examination. 
• You can download the NCERT Solutions for free in pdf format and access them whenever you want. 
• You can practice the NCERT Solutions at your own pace without any rush and study independently. 

NCERT Class 10 Maths Chapter 6 Triangles FAQs

1. How many questions are there in NCERT Class 10 Maths Chapter 6 Triangles?

NCERT Chapter 6 Triangles of Class 10 Maths includes 14 solved examples and 65 unsolved problems. There are 6 exercises in this chapter and all are important from the exam perspective. 
 

2. What are the important topics covered in NCERT Class 10 Maths Chapter 6 Triangles? 

Class 10 Maths Chapter 6 Triangles includes many important theorems related to the similarity of triangles. Criteria for similarity of triangles and areas of similar triangles are two important topics for the Class 10 board examination from this chapter. 
 

3. How many theorems are there in NCERT Class 10 Maths Triangles chapter? 

There are 9 theorems included in NCERT Class 10 Maths Triangles chapter. Some of them are the Pythagoras Theorem, the converse of Pythagoras Theorem, Baudhayan Theorem, Basic Proportionality Theorem (Thales Theorem), and the converse of Basic Proportionality Theorem.