Pythagoras
The entire transcript is given below.Hello students, welcome to the channel Omega Minds. So our topic today is Pythagoras theorem.
It is a very important topic for grade seven. Now, we think Pythagoras theorem is a very difficult topic, but let us try to understand it in a simple way. Pythagoras was actually a Greek philosopher who made a huge contribution to mathematics, astronomy and music.
We believe that this theorem was known to the Babylonians at least a thousand years ago. But Pythagoras was the first person to prove this theorem mathematically. So, let us see how he proved it. So, as you can see on the screen, there is a triangle and we have named the sides of that triangle as sides A, B and C. So, you can see which is the longest side. Yes, correct, it is C, which we call the hypotenuse. Two sides are left which are a and b.
So, this theorem says that if we find the longest side, then If we square the side, then the answer should be equal to If we square the remaining two sides and add them, then if we calculate it mathematically, it becomes that the square of the hypotenuse is equal to the square of a, which is your perpendicular and height plus the square of b, which we call the base.
So, if we write it mathematically, our formula will become cs = as + b square Where a is your perpendicular, b is your base and c is your height tensor. I hope till here you have understood the structure of what the Pythagoras theorem tells us.
Now I will tell you one more condition. The Pythagoras theorem which will be applied will always be applicable to a 90-degree triangle. What does it mean that you can easily apply this theorem on any triangle which is formed in 90 degrees. So, now let us move on to a question in which we try to know whether this actual How will we check whether the theorem is applicable to this particular triangle or not? For example, you are seeing a triangle on the screen. It has three sides - the first side, which we call perpendicular, and the height.
There, we have been given 12 as the base, which is given five. And we have the hypotenuse, which is 13. So now we have to apply this theorem and check whether this theorem is applicable to this triangle or not. We have just read the formula earlier, which is cs = as + bs, where c means the hypotenuse, which is 13 given in this question. And we are considering a as perpendicular, which is given 12, and b as the base, which is five. So now what we do is, we simply put these values in this formula and find their square. So, in place of c, we have put 13, and in place of b, we have put When we squared 12 and 5, 12, we get 144. When we squared 5, we are getting 25. And what we had to do was add these two, so our answer should be equal to the square of 13.
So, if we can see that 169 is coming equal to 169, it means that this theorem is being applied. So, now we have said that this theorem is being applied. What is its conclusion? Its conclusion is that if Pythagoras theorem is being applied on any triangle, then it means that the triangle is a right-angled triangle, it is very important ifIt will be a right angle triangle.
You have been given a right angle triangle in the question. So you can apply Pythagoras. If you apply Pythagoras and it gets solved, then it means what kind of triangle it is. By default, it is a 90° triangle. So, in your book, you will find a question like identifying which right side is coming equal to the right side.
So, it means that it is a right angle triangle. Now the question arises that which value should be considered as perpendicular, which value as base and which value as hypotenuse. If this question is coming in your mind, then you are going on the right track. What is the solution for this? So, we will consider the longest side as the longest side. Like here, 13 is given in the figure. If you do not have that figure and you are given only the three sides, 12, 13 and five, then the largest side will automatically be considered as the hypotenuse. And we will square the remaining two sides and find their sum. We will find it out. I hope if this doubt is there in your mind then it should be cleared now.
Next let's move on to a question where we are given two values, two sides are given but we don't know the third side. So what we have to do is apply the formula - the square of hypotenuse equals the square of perpendicular plus the square of the base. Say it with me once again - the square of hypotenuse equals the square of perpendicular plus the square of the base. So what did we do? We just put in the values that were given to us and tried to find our answer. So what did we do? We put t in place of perpendicular and squared it.
We put 15 in place of base and squared it. It is equal to the square of hypotenuse. Now we don't know what the hypotenuse is, so we considered it as x and squared it. We solved the values. See what the square of 8 is. Look at the screen, 64 is written. What the square of 15 is. It is 225. You will get if you add it. 289 Now you think that the question has been solved here, no, it is not like that yet, we have got xs = 289 but what do you want to find, you have to find the value of x, so you must remember the method of prime factorization, so when you do the prime factorization, you will get 289, which is the square of 17, so 17 is the answer for the value of a, I hope the doubt is clear, if you have any questions, please let me know in the comments section, thank you for watching .We will consider it as the hypotenuse and square the remaining two sides and find their sum. I hope if you have this doubt in your mind, it should be cleared by now.
Next, let's move on to a question where we are given two values. Two sides are given but we don't know the third side. So what we have to do is apply the formula - the square of the hypotenuse equals the square of the perpendicular plus the square of the base. Say it with me once again - the square of the hypotenuse equals the square of the perpendicular plus the square of the base.
So what did we do? We just put in the values that were given to us and tried to find our answer. So what did we do? We put t in place of perpendicular and squared it. We put 15 in place of base and squared it. This is equal to the square of the hypotenuse. Now, we don't know what the hypotenuse is. So we considered it as x and squared it. We solved the values. See what the square of 8 becomes.
Look at the screen. 64 It is written what is the square of 15, it is 225, if you add it you will get 289 now you think that the question has been solved here, it is not like that yet, we have got xs = 289 but what do you have to find, you have to find the value of x, so you must remember the method of prime factorization, so when you do prime factorization then you will get 289 which is becoming the square of 17, so 17 is the answer for the value of a, I hope the doubt is clear if you have any questions please let me know in the comment section, thank you for watching .
We will consider it as the hypotenuse and square the remaining two sides and find their sum. I hope if you have this doubt in your mind, it should be cleared by now. Next, let's move on to a question where we are given two values. Two sides are given but we don't know the third side.
So what we have to do is apply the formula - the square of the hypotenuse equals the square of the perpendicular plus the square of the base. Say it with me once again - the square of the hypotenuse equals the square of the perpendicular plus the square of the base. So what did we do? We just put in the values that were given to us and tried to find our answer. So what did we do? We put t in place of perpendicular and squared it. We put 15 in place of base and squared it.
This is equal to the square of the hypotenuse. Now, we don't know what the hypotenuse is. So we considered it as x and squared it. We solved the values. See what the square of 8 becomes. Look at the screen. 64 It is written what is the square of 15, it is 225, if you add it you will get 289 now you think that the question has been solved here, it is not like that yet, we have got xs = 289 but what do you have to find, you have to find the value of x, so you must remember the method of prime factorization, so when you do prime factorization then you will get 289 which is becoming the square of 17, so 17 is the answer for the value of a, I hope the doubt is clear if you have any questions please let me know in the comment section, thank you for watching.
I'll summarize the key points from the Hindi/English mixed
language video about the Pythagorean theorem:
- The
video introduces Pythagoras as a Greek philosopher who made significant
contributions to mathematics, astronomy, and music
- While
the theorem was known to Babylonians at least 1000 years earlier,
Pythagoras was the first to mathematically prove it
- The
theorem states that in a right triangle, the square of the hypotenuse (c)
equals the sum of squares of the other two sides (a and b), written as c²
= a² + b²
- The
theorem only applies to triangles with a 90-degree angle
- The
video demonstrates the application using a triangle with sides 12, 5, and 13
- When
given three sides, the longest side is always the hypotenuse
- The
video shows how to verify if a triangle is a right triangle by applying
the theorem
- If
the theorem's equation holds true for a triangle, it confirms the triangle
is a right triangle
- The
video explains how to find an unknown side length using the theorem
- It
concludes with working through an example where one side needs to be
calculated using prime factorization, resulting in 17 as the answer