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NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.6

 

NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.6 are created by the askIITians Maths experts to help you understand important concepts of triangles. Chapter 6 Triangles of Class 10 Maths is based on the concept of congruence of triangles. 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. 

 

The askIITians Maths experts have created NCERT Solutions for Chapter 6 Triangles Ex 6.6 with comprehensive explanations and proper reasoning. Students can study these solutions independently at their own pace. Our solutions are self-explanatory which means that you need no further guidance in understanding the concepts of this chapter. Let us see what is included in this exercise and how you can download the NCERT Solutions. 

About NCERT Class 10 Maths Chapter 6 Triangles Ex 6.6 

 

The last exercise of the Triangles chapter is an optional exercise which is why not many students practise it. However, we recommend that you must practise the questions of this exercise before exams to strengthen your concepts of the chapter. This exercise is based on all the topics and theorems that you have studied in this chapter. The questions of this exercise are of advanced level which will test how well you understand the concepts of similarity of triangles. 

 

Important points related to Ex 6.6 of Chapter 6 Triangles:

 

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 Ex 6.6 

 

This exercise covers the scope of solving the entire chapter. This will boost your confidence and make it easier for you to score full marks in the chapter in the exams. Do not leave this exercise just because it is optional. In case you have any doubts, our NCERT Solutions will help you resolve them. Here are some other important features of our NCERT Solutions for Chapter 6 Ex 6.6: 

 

  • All the NCERT Solutions for Ex 6.6 include stepwise explanations and proper reasoning. 
  • The NCERT Solutions are based on the latest CBSE exam pattern and syllabus for Class 10 Maths. 
  • We have also included proper diagrams so that students can understand the NCERT questions thoroughly. 
  • These solutions will provide you with the right approach to solving questions based on triangles and their similarity. 
  • The solutions include all the steps so that students can understand how to solve the questions in the exam and earn full marks. 

 

Tips on solving the optional exercise 6.6 questions of Class 10 Maths Chapter 6: 

 

  • Make sure you understand all the theorems of this chapter before you start solving this exercise. 
  • Read the questions carefully and take note of all the important points for solving the questions. 
  • Draw a labelled diagram for the question to help you understand how to solve the question. 
  • Develop a habit of solving the questions step by step so that there is the minimal scope of losing marks in the examination. 

NCERT Class 10 Maths Chapter 6 Triangles Ex 6.6 FAQs

 

1. How many questions are there in NCERT Ex 6.6 of Class 10 Maths?

There are 10 unsolved questions in NCERT Class 10 Maths Chapter 6 Ex 6.6. The askIITians experts have solved these questions stepwise to help you understand all the concepts of this chapter thoroughly. 

 

2. How to study NCERT Class 10 Maths Chapter 6? 

Use askIITians revision notes, extra questions, mind maps, flashcards, previous year questions, important questions, practise papers, NCERT Solutions, and many different study resources to master Chapter 6 Triangles. 

 

3. I need more help with NCERT Class 10 Maths. What should I do? 

You must enrol in askIITians online Maths coaching. We provide regular, live, interactive online classes to Class 10 students where you can prepare for the Class 10 board examination with our Maths experts. 


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