 Hi and welcome to the session. Today we will learn about right-angled triangles and Pythagoras property. Here we have a triangle A, B, C, right-angled at V. So triangle A, B, C is a right-angled triangle. Now the sides of a right-angled triangle have some special names. The side opposite to the right angle is known as hypotenuse. So here angle B is a right angle and the side AC is the side opposite to the right angle that is angle B. So here for the triangle A, B, C, right-angled at B, AC is the hypotenuse and the other two sides are known as the legs of the right-angled triangle. So here side A, B and side B, C are the legs of the right-angled triangle A, B, C. Now let's see the Pythagoras property. This states that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the legs. So here in the right-angled triangle A, B, C according to the Pythagoras property we have AC square is equal to AB square plus VC square. Now this means for a right-angled triangle the Pythagoras property will hold and if the triangle is not a right-angled triangle then the Pythagoras property will not hold good. Now conversely we also have if the Pythagoras property holds then the triangle must be right-angled. This property is useful to decide whether the given triangle is a right-angled triangle or not. Let's take an example for this. We are given the length of three sides of a triangle as 6 centimeter, 8 centimeter and 10 centimeter and we need to determine whether the given triangle will be a right-angled triangle or not. So for this first of all let us find out the squares of all the three sides of this triangle. So 6 square is equal to 36, 8 square is equal to 64 and 10 square is equal to 100. Now it is very clear that 100 is equal to 64 plus 36. So that means 10 square is equal to 8 square plus 6 square. So from this we can see that the Pythagoras property is satisfied. That means the given triangle is a right-angled triangle. Now hypotenuse is the longest side of the triangle. So here for this triangle the side with length 10 centimeters will be the hypotenuse. Now let's take one more example. Suppose we are given the triangle ABC right-angled at B with length of the side AC that is hypotenuse as 41 centimeters and the length of the side BC as 40 centimeters and we need to find the length of the side AB. So for this we will use the Pythagoras property and according to Pythagoras property we have AC square is equal to AB square plus BC square. Now substituting the values we will get AC square that is 41 square is equal to AB square plus BC square that is 40 square. This implies AB square is equal to 41 square minus 40 square which will be equal to 1,681 minus 1,600 that is 81 which is equal to minus square. That means AB is equal to 9 centimeters. Thus in this session we have learnt about right-angled triangles and Pythagoras property. With this we finish this session. Hope you must have enjoyed it. Goodbye, take care and keep smiling.