NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.5 are the best study material for board exam preparation. The fifth exercise of Chapter 6 Triangles of Class 10 Maths is based on the Pythagoras Theorem. You must already be familiar with this theorem from earlier classes. But, in class 10 you will study how to prove the Pythagoras Theorem using the concept of similarity of triangles.
askIITians Maths experts have prepared stepwise solutions for NCERT Exercise 6.5 of Class 10 Maths Chapter 6. These solutions are based on the latest CBSE exam pattern and help you understand how to approach the questions related to Pythagoras Theorem in the examination. Let us see what is included in this exercise and how you can download the NCERT Solutions for free.
Important theorems related to Ex 6.5 of NCERT Class 10 Maths Chapter 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 to 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).
Types of questions included in NCERT Class 10 Maths Chapter 6 Ex 6.5:
There are a variety of questions included in this exercise and all of them are important from the exam point of view. This exercise includes 17 questions out of which at least 14 questions are in the form of word problems. This means you have to read them, analyse them and then formulate a solution.
Some questions in this exercise are easy to solve where you are given the three sides of a triangle and you have to prove whether it is a right-angled triangle or not. For example, in question number 1, you are given sides of different triangles and you have to determine which of them are the right triangles.
Some questions in this exercise ask you to prove that the given triangles are the right triangles. For example, in question number 5 you are given that ABC is an isosceles triangle with AC = BC. If AB2 = 2 AC2, you have to prove that ABC is a right triangle.
Another category of questions included in Ex 6.5 of Class 10 Maths Chapter 6 is based on the application of the Pythagoras Theorem. For example, in question 6 you are given that ABC is an equilateral triangle of side 2a. You have to find each of its altitudes. Questions 9 to 12 are also based on the application of the Pythagoras Theorem.
Tips on how to solve the exercise questions of NCERT Class 10 Maths Chapter 6 Triangles Ex 6.5:
Make sure you understand how to apply the Pythagoras Theorem or its converse.
In case of long word problems make sure you write down all the information given to you and then approach the solution.
Draw a rough diagram of the question to get a better understanding of what you have to do.
In case of any doubts, refer to our stepwise NCERT Solutions for Class 10 Maths and resolve your queries.
Practice all the questions of the exercise whether they are long answer type or short answer type questions.
We have provided stepwise solutions for this exercise in PDF format. You can download the NCERT Solutions pdf and refer to them whenever you want. This way you can learn independently and study at your own pace. Since there are 17 questions in this exercise, we do not expect you to practise them all in one go. You must solve every question carefully and then gradually increase your problem-solving speed.
Highlights of NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.5:
The NCERT Solutions include proper explanations and reasoning for every question for your better understanding of the Pythagoras Theorem and its converse.
You can download the exercise-wise solutions for NCERT Class 10 Maths Chapter 6 and study them at your own pace.
Each solution is checked at least twice by our experts to make sure that it is correct and updated.
The solutions are based on the NCERT Class 10 Maths syllabus and exam pattern provided by CBSE.
The NCERT Solutions are the perfect study guide for the students for board exam preparation.
Download free NCERT Solutions for all exercises of Class 10 Maths Chapter 6 Triangles:
NCERT Chapter 6 Class 10 Maths Ex 6.1 Solutions - 3 Questions
NCERT Chapter 6 Class 10 Maths Ex 6.2 Solutions - 10 Questions
NCERT Chapter 6 Class 10 Maths Ex 6.3 Solutions - 16 Questions
NCERT Chapter 6 Class 10 Maths Ex 6.4 Solutions - 9 Questions
NCERT Chapter 6 Class 10 Maths Ex 6.5 Solutions - 17 Questions
NCERT Chapter 6 Class 10 Maths Ex 6.6 Solutions - 10 Questions
1. How many solved examples are there in Ex 6.5 of Class 10 Maths Chapter 6?
There are 5 solved examples for NCERT Class 10 Maths Ex 6.5 that will help you understand how to solve the NCERT exercise questions. You must practise these 5 solved examples first and then start solving the NCERT Ex 6.5.
2. How to study NCERT Class 10 Maths Chapter 6 Triangles?
askIITians provides a plethora of study resources for students so that they can revise every concept of Class 10 Maths thoroughly. For Chapter 6, we have revision notes, extra questions, sample papers, practice worksheets, mind maps, flashcards, and NCERT Solutions for your practice. Download them from our website and start learning.
3. I need more help with NCERT Class 10 Maths. What should I do?
Join online coaching classes for Class 10 Maths at askIITians and get personalised coaching from our experts. Our live, interactive classes provide a classroom-like environment to the students and at the same time give them certain control over their learning. Find more about our latest courses on our website.