 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says APCD is a parallelogram and AP and CQ are perpendicular from vertices A and C on diagonal BD show that first is triangle APB is congruent to triangle CQD and second is AP is equal to CQ. So here we are given that APCD is a parallelogram, AP is perpendicular on BD also CQ is perpendicular on BD and we have to prove that triangle APB is congruent to triangle CQD. Let us try to prove it. It is considered in triangles APB and triangle CQD. Now in these two triangles is equal to CD since opposite sides of the parallelogram are equal also angle APB is equal to angle CQD is equal to 90 degree since AP is perpendicular on BD and also CQ is perpendicular on BD. BP is equal to angle CDQ since DC is parallel to AB since ABCD is a parallelogram. BD is any transversal then is equal to this angle since interior angles are equal and here since DC is parallel to AB and BD is a transversal therefore alternate interior angles are equal hence these two angles are equal and since when two angles of a triangle are equal to the corresponding two angles of other triangle then the third angle is also equal therefore we can say by AC congruence condition triangle ABP is congruent to triangle CQD. So this is the first one we have to prove that AP is equal to CQ. Now since triangle APB is congruent to triangle CQD as we have proved above so this implies AP is equal to CQ by CPCT that is corresponding parts of congruent triangles are equal so this completes the session hope you enjoyed it take care and have a good day.