 Hello and welcome to the session. In this session we discussed the following question which says t and s are points on the sides qp and qr of a triangle pqr. Right angled at q proves that ps square plus rt square is equal to pr square plus ts square. Now let's see the solution. Here we are given a triangle pqr in which angle q is equal to 90 degrees. Then t is a point on the side pq and s is a point on the side rq and we need to prove ps square plus rt square is equal to pr square plus rt square plus rt square plus rt square plus ts square. First of all consider the right triangle pqs in this we have ps square is equal to pq square plus qs square. This is by the Pythagoras theorem. Let this be equation 1. Then next we consider the right triangle trq in this tr square is equal to tq square plus qr square. This is also by the Pythagoras theorem. Now consider the right triangle trq in this tr square is equal to pq square plus qr square by the Pythagoras theorem. Take this as equation 3. Then next consider the right triangle trq in this consider the right triangle tsq in this st square is equal to sq square plus qt square. This is again by the Pythagoras theorem. We take this as equation 4. Now we add equations 1 and 2. So adding equations 1 and 2 we get a square plus tr square is equal to pq square plus qs square plus tq square plus qr square. That is we get ps square plus tr square is equal to pq square plus qr square plus qs square plus tq square or you can say s square plus tr square is equal to pq square plus qr square plus sq square plus qr square plus qr square Now from equation 3 as you can see we have pr square is equal to pq square plus qr square. So here we put pr square and from equation 4 we have st square is equal to sq square plus qt square. So here we will put st square. So in this way we get s square plus tr square is equal to pr square plus st square or you can say we get ps square plus rt square is equal to pr square plus ts square. We were supposed to prove this and so hence proved this completes the session. Hope you have understood the solution of this question.