 Hi and welcome to the session. I am Priyanka and let us discuss the following question. It says show that in a right angle to triangle, the hypotenuse is the longest side. But before proceeding on with the solution, we should be well versed with a theorem that says in any triangle, the side, the larger, this means that if we have a triangle, let's say triangle A, B, C, then the side opposite to the larger angle, let us say that C is the largest angle. The side opposite to the larger angle is the longest side. So here, if angle C is greatest angle, greater angle, then this is an example which explains this theorem very well. So the knowledge of this theorem is the key idea that we are going to use in order to proceed on with our solution. Now here, let us have a right-angled triangle first. Let this be angle 1, this be a second angle and this be a third angle and this is angle A, B, C which is right angled at B. So in this question, we are given that in right triangle, B is equal to 90 degrees. This is what is given to us in the question. We need to prove that hypotenuse C is the longest angle that is. We need to prove that AC is greater than AB and also AC is greater than BC. So let us start with our proof. Now, we know that in triangle A, B, C, angle A, B, C is equal to 90 degrees. Let us draw this diagram once again. Angle A, B, C is equal to 90 degrees. This is given to us in the question. But if you see angle 1 plus angle 2 plus angle 3 is equal to 180 degrees because the sum of all angles of a triangle is 180 degrees. Now angle 2 is given to us as 90 degrees. So that implies angle 1 plus 90 degrees plus angle 3 is equal to 180 degrees. Or we can say angle 1 plus angle 3 is equal to 180 degrees minus 90 degrees. That means it is equal to 90 degrees. So this implies that angle 1 and angle 3 are acute angles. Angle 1 is less than 90 degrees and also angle 3 is less than 90 degrees. Since angle 1 is less than 90 degrees, but we know that angle 2 is equal to 90 degrees, we can write that angle 1 is less than angle 2 and angle 3 is less than angle 2. This implies that is greater than AP because AC is the side opposite to angle 2 and is greater than opposite to larger. So according to the key idea or the theorem that we started in our key idea that side opposite to greater angle is larger, this proves that AC is greater than AB and AC is also greater than BC. So therefore we can write that hence it proves that hypotenuse is the longest side. So this ends the question that was given to us. I hope you enjoyed this session. Bye for now.