What is Pythagoras Theorem? | Explanation of Pythagoras Theorem | Geometry | Math | Letstute

Triangles. Three sides and three angles. Friends, in our previous session we played with the sides and angles of triangles to analyze different situations where they can be proved similar and congruent. So in this session we'll study something more about it. We can see some triangles on the screen. In one of the triangles instead of small arc we can see a small square. Why is this so? This small square denotes an angle measurement of 90 degrees and we know that in a square and a rectangle all the four angles are of 90 degrees. So this could be the reason why we denoted by a small square or say a small rectangle. Therefore when we see this symbol it is understood that its measure is 90 degrees. Friends, it is also known as a right angle and a triangle with one angle as 90 degrees is known as a right angled triangle. One of the well-known and the most interesting property of a right angled triangle involves only its three sides and it says that when we square its longest side or what we generally call a hypotenuse its value is always equal to the sum of these squares of the remaining two sides and this property is really important as we use it frequently in maths and has many real life uses too. For example, think of this situation if the door of your house is not opening for whatsoever reasons then the other choice you might want to consider would be probably to get in through the window which is say 16 feet above the ground. Now to your surprise you also find a 20 feet ladder lying nearby. So obviously the first thing that anyone would try will be to place the ladder appropriately along the wall, climb it and reach the window. In the process as we can see in this arrangement the ladder, ground and the wall together make a right angled triangle where the ground acts as the base and the wall seems to be the perpendicular height of this triangle so formed and with the help of the relation that we discussed just now we can certainly decide at what distance from the building the ladder should be placed so that it can touch the window. Now this was a small example to give you all an idea. Besides this architects, carpenters and contractors also use it on a daily basis like in laying the foundation of a building to make each corner a perfect right angle. This unique property of a right angled triangle was first proved by the Greek mathematician Pythagoras and hence is universally known as Pythagoras theorem. But what does squaring the hypotenuse and sides mean? Let me explain it in detail. Suppose we draw a square whose side is same as the length of the hypotenuse then we'll find its area. It will actually be equal to side length square and since this length in this case is hypotenuse so we can call it hypotenuse square. In the same way if we draw squares even on the other two remaining sides their areas will be equal to the square of these respective sides. So geometrically it means that the sum of the areas of two squares built on shorter sides is equal to the area of the square built on the hypotenuse. Friends now you must have understood that this power 2 which we call square actually refers to the area. Now we can see these all are same shape that is a square but of different sizes and we have learnt in our previous session that whenever two or more things have same shape but only refers with respect to their size then they are called similar. But what do you think can we draw only squares on the sides of right angle triangles? So let me tell you we can draw any two-dimensional shape say a semicircle a triangle or any other shape on the sides of right angle triangles as long as the figures are similar they will always satisfy the Pythagoras theorem relation. But the question is will the Pythagoras relation hold true even if a triangle is not a right angle triangle? No and to analyze this let's consider these triangles we will draw squares on their sides and find out their areas. Here we realize that the area of the bigger square is not equal to the sum of the areas of the two smaller squares. So friends we can conclude that the Pythagoras theorem does not stand true for triangles other than right angle triangles. I hope we all have understood the things we have learned so far. So let's do a small recap we started with the basic properties of triangles then we learned that only right angle triangles have a unique property universally known as Pythagoras theorem. We also understood that the squares of the sides of right angle triangles actually relate to the areas of the figures drawn on it and finally we concluded that not necessarily only squares but we can draw any similar shapes on the sides of right angle triangle and it will still satisfy the relation. So friends as now we all have understood the Pythagoras theorem and the logic behind it. In our next session we'll learn its detailed proof but still if you have any doubt or query regarding any concept of maths please comment us in the below comment box or you can also whatsapp us and if you really liked it do like and share with your friends. To get more such videos kindly subscribe to our channel let's do