 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says, A B C D is a rectangle in which diagonal A C bisects angle A as well as angle C show that first A B C D is a square second diagonal B D bisects angle B as well as D. So here in this question we are given a rectangle in which the diagonal A C bisects angle A as well as C. So this implies angle D A C is equal to angle C A B and angle D C A is equal to angle B C A. So first let us write down what we are given. So we are given a rectangle A B C D in which angle D A C is equal to angle B A C and angle D C A is equal to angle B C A and we have to prove A B C D is a square. So let us begin with the proofs, triangle B C B C angle D A C is equal to angle B A C this is given. So angle D C A is equal to angle B C A equal to C A. This side is common to both the triangles. Therefore by A C congruence condition D C is congruent to triangle A B C which implies A D is equal to A B D C is equal to B C. This is by C bisect. That is corresponding parts of congruent triangles are equal. Also so this implies opposite sides are equal that is A D is equal to B C and A is equal to D C. Now from this and this we conclude that A B is equal to C D B C and B C is equal to this implies all the four sides of this rectangle are equal. This implies that A B C D is a square. So this completes the first part. Second part we have to prove that diagonal B D bisects angle B equal to angle D. That is have to show that angle A B D is equal to angle C B D. These two angles and angle A D B and angle C D B are equal. Now let us consider triangle B C D and triangle B A D. Now in these two triangles side A D is equal to D C since A B C D is a square and all the sides of a square are equal. Also A B is equal to B C. Again since A B C D is a square and all the sides of a square are equal so these two sides are also equal and B D is equal to D B. This is common to both the triangles. Therefore by SSS congruence condition triangle B C D is congruent to triangle B A D which further implies that angle A B D is equal to angle C B D and angle A D B is equal to angle C D B. This is by C B C D that is corresponding parts of congruent triangles are equal which further implies that diagonal B D vice its angle B as well as angle T. So this completes the session. Take care and have a good day.