 Hello and welcome to the session. In this session we discuss the following question which says, in the given figure A B C is a triangle right angled at B if B C D E is a square on side B C and A C S G is a square on A C prove that A D is equal to B F. Before moving on to the solution let's recall the S A S congruence rule. According to this we have if two sides and the included angle of one triangle are equal and the included angle of the other triangle, the two triangles are congruent. This is the key idea for discretion. Now we move on to the solution. This is the figure given to us. In this we are given that A B C is a right angled triangle right angled at B that is we are given angle A B C equal to 90 degrees. We are also given that B C D E is a square on side B C and A C S G is also a square on side A C. We need to prove that A D is equal to B F. Now we consider the triangles A C D and F C D. Now angle A C D as you can see in the figure is equal to angle B C D plus angle A C D and angle F C D is equal to angle F C A plus angle A C B. Now since B C D E is a square so all its angles would be of measure 90 degrees and angle B C D is an angle of the square B C D E so it would be of measure 90 degrees. So we say this is equal to 90 degrees plus angle A C B that is angle A C D is equal to 90 degrees plus angle A C B. Now A C F G is also a square so all its angles would be of measure 90 degrees and angle F C A is an angle of the square A C F G so it would be of measure 90 degrees. So this is equal to 90 degrees plus angle A C B. So therefore we now get angle A C D is equal to angle F C B. Then we have side C F of the triangle F C B is equal to the side C A of the triangle A C D since they are the sides of the square A C F G. Then we have then we have the side C D of triangle A C D is equal to the side C B of triangle F C B since they are the sides of the square B C D E. Thus from here we conclude that triangle A C D is congruent to triangle F C B by S A S congruence rule. Now since both these triangles are congruent so their corresponding parts would be equal that is we now get A D is equal to B F since they are the corresponding parts of the congruent triangles so they are equal and we were supposed to prove this only. So hence proved this completes the session hope you have understood the solution for this question.