NCERT Solutions for Class 10 Maths Chapter 6 Triangles (Ex 6.5) Exercise 6.5

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NCERT Solutions for Class 10 Maths Chapter 6 Triangles (Ex 6.5) Exercise 6.5

Our team at Vedantu is always striving to create the most reliable and beneficial solutions for students and our NCERT Solutions Class 10 Maths Ex 6.5 is an example of the same. The way our subject matter experts have given Ex 6.5 Class 10 Maths NCERT Solutions, even those of you who find Mathematics difficult would start enjoying the subject. These accurate and error-free Maths Class 10 Chapter 6 Exercise 6.5 solutions are based on the latest CBSE curriculum so that you can expect high scores in maths by availing these solutions. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution Class 10 Science, Maths solutions, and solutions of other subjects.

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Chapter 6-Triangles part-1

CBSE Class 10 Maths Chapter 6 Exercise 6.5 Solutions Free PDF

Now you can get answers to every question in Class 10 Maths Chapter 6.5 in PDF format on the official website of Vedantu. These PDFs can be downloaded anytime anywhere on your device or printed out, and then you can access them without an internet connection. The NCERT Class 10 Ex 6.5 PDF is the easiest and quickest way to revise all the formulas and tips for the Pythagorean theorem and its applications.


Class 10 Maths Exercise 6.5 Solutions

Exercise 6.5 Class 10 Question 1

The first question of Ex 6.5 Class 10 has measurements of the sides of 4 different triangles. For each of them, you need to apply the Pythagoras theorem to determine if they are right-angled triangles or not. You also need to calculate the hypotenuse of the right-angle triangles.


Exercise 6.5 Class 10 Question 2

A pictorial diagram of a triangle PQR (right-angled at P) is presented to you in this question of 6.5 Exercise Class 10. A perpendicular PM is dropped from P to the side QR, and you need to prove them PM² = MQ * MR. This can be done by using the AAA similarity criterion and concept of Pythagoras theorem.


Exercise 6.5 Class 10 Question 3

In the 3rd question of maths Class 10 6.5, a triangle ABC is given along with 3 statements regarding its sides. You need to prove those statements by using AA and AAA similarity criteria. If you prove the first two statements, the third statement gets proved automatically.


Exercise 6.5 Class 10 Question 4

Maths Class 10 Ex 6.5 question 4 has an isosceles triangle ABC which is right-angled at C. You need to prove that AB² = 2*AC² and you can prove this by the simplest form of application of the Pythagoras theorem.


Exercise 6.5 Class 10 Question 5

This question again has an isosceles triangle where AC = BC. You need to prove that it is a right-angle triangle by applying the converse of the Pythagoras theorem. You could use the knowledge gained in class 10 about triangles to solve this question.


Exercise 6.5 Class 10 Question 6

This question presents a triangle ABC in a diagram that has sides = 2a. Students have to find the length of each of the altitudes. You can do this by drawing a perpendicular AD from A on side BC and apply the theorem that the altitude of an equilateral triangle bisects the opposite sides. Along with this feature of an equilateral triangle, you also need to use the Pythagorean theorem to answer this question.


Exercise 6.5 Class 10 Question 7

Here you need to prove that in a rhombus the sum of the square of its sides is equal to the sum of squares of its diagonals. This needs the application of your knowledge in equilateral triangles and the Pythagoras theorem to prove this statement.


Exercise 6.5 Class 10 Question 8

Question 8 in exercise 6.5 Class 10 Maths requires basic concepts of triangles to prove two relations given. Approach this problem in a step-by-step manner, and you can easily do it.


Exercise 6.5 Class 10 Question 9

It is a practical problem involving a ladder which is put against a window, and you need to find the distance of the foot of the ladder from the base of the wall. This question tests your aptitude in trigonometric derivatives, and you need to apply the Pythagoras theorem to calculate the height and distance.


Exercise 6.5 Class 10 Question 10

You can solve this question if your core knowledge of Pythagoras theorem is strong. It is a practical problem that is a bit tricky; hence just knowing the theorem would not suffice. With our diagrammatic approach to the question, you should be able to understand the derivation clearly.


Exercise 6.5 Class 10 Question 11

The central idea of the 10th question is combining your knowledge of trigonometry with the Pythagoras theorem. It is again a practical problem where two aeroplanes’ speed, flying North and West is given, and you need to find the distance between the two planes after a certain time lapse.


Exercise 6.5 Class 10 Question 12

This is another problem that contains the application of both Pythagoras theorem and trigonometry concepts. Your ease in such problems will develop as you keep doing such problems and building your foundation in both these aspects of mathematics.


Exercise 6.5 Class 10 Question 13

In a right-angled triangle, ABC, right-angled at C, two points D and E are taken on sides AC and BC respectively. One needs to prove equations involving the interrelation of triangles and the Pythagoras theorem.


Exercise 6.5 Class 10 Question 14

This question needs an elaborate implementation of the Pythagoras theorem and is a lengthy problem where you are given the figure of a triangle ABC. A perpendicular is drawn from point A on BC which intersects the side at D, and you need to prove a statement involving these sides of the triangle.


Exercise 6.5 Class 10 Question 15

Question 15 of this exercise is based on an equilateral triangle, and you are given various features of that triangle. It is one of the complicated problems, but you can easily understand it once you go through our solutions. You would need to draw an imaginary altitude from A to BC. Then you can apply the property of the altitude of an equilateral triangle that bisects the opposite side to derive the equation given.


Exercise 6.5 Class 10 Question 16

This question requires you to prove some facts about an equilateral triangle. You need to prove that in an equilateral triangle if you multiply the square of one side by 3 then it is equal to 4 times the square of one of its altitudes.


Exercise 6.5 Class 10 Question 17

The last question is a multiple-choice question where you need to find out one specific angle of a triangle. You are given the length of the sides of the triangle and apply Pythogaros triplets to find the solution.


Key Features of NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.5

The NCERT Solutions Class 10 Maths Ex 6.5 is prepared by the expert team of Vedantu keeping in mind the understanding level of class 10 students. Hence students will find it easy to go through them. Some of the main benefits of these solutions are:

  • The solutions will clarify your doubts at the root level so that you can successfully attempt similar problems independently.

  • The answers to each question are there, and nothing is left out.

  • The mathematicians at Vedantu have taken care of the CBSE pattern and NCERT guidelines to answer these questions so you can be sure of scoring good marks with our solutions.

  • Having the solution in PDF format is very convenient for quick revisions.

FAQ (Frequently Asked Questions)

Q1. What is the Main Topic of Exercise 6.5 of Class 10th Maths, Chapter 6?

Ans. Exercise 6.5 of chapter 6 of class 10th maths is based on theorems involving right-angled triangles. The basis of the problems is the Pythagoras theorem along with many concepts you have learned about triangles in previous chapters. There are questions based on equilateral triangles, isosceles triangles, etc. for which you need to remember formulas or theorems revolving around these special triangles.

Q2. State the Pythagoras Theorem.

Ans. The Pythagoras theorem in mathematics denotes the fundamental relation between the three sides of a right-angle triangle. According to the Pythagoras theorem, in a right-angle triangle, the value of the square of the hypotenuse (this is the side opposite to the angel which is 90°) is equal to the summation of the squares of the other two sides so if ABC is a triangle where angle C is 90 degrees then:

AB² = BC² + AC².

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