 Hi and welcome to the session. I am Priyanka and let us discuss the following question. It says AB and CD are respectively the smallest and longest side of a quadrilateral ABCD, C figure 7.50. Show that angle A is greater than angle C and angle B is greater than angle T. Now this is figure 7.50 which we need to refer. Let us start with our solution. It's given to us that AB and CD are the shortest and longest sides of a quadrilateral. We need to prove angle A is greater than angle C and angle B is greater than angle D. So for that we need to do a little bit of construction. First of all we need to join AC and then we need to join BD. Let us draw the given figure once again. This is AB, C and D. Let us start with our proof. First of all let us join AC. Let us name this angle as angle 1, this as angle 2, angle 3 and angle 4. Now it's given to us that AB is the shortest side that means AB will be smaller than BC also. So therefore angle 2 will be less than angle 1 because sides opposite to or angles opposite to greater sides are greater. So the angle opposite to BC is angle 1. Therefore angle 1 is greater than angle 2. Similarly in triangle ACD, CD is greater than AD let us say because CD is the longest side so it will be longer than AD also. So therefore angle 4 is greater than angle 3 because of the same reason that angles opposite to greater sides greater. Now on adding 1 and 2 we have angle 2 plus 3 is less than angle 1 plus angle 4, angle 2 plus angle 3 is angle C is less than angle A or angle A is greater than angle C. So this proves one of the parts of the question. Proceeding on with the question again let us draw the diagram once again. Now let us join BD and let us name it as 5, 6, 7 and 8. Now AB is smaller than AD therefore we can say that angle 7 is greater than angle 5 because of the same reason that is angles opposite to greater sides greater. Similarly we are having the knowledge that CD is greater than BC in triangle CDB. So therefore angle 8 will be greater than angle 6. On adding 3 and 4 we have angle 7 plus angle 8 is greater than angle 5 plus angle 6. Angle 7 plus angle 8 is angle B is greater than angle 5 plus angle 6 is angle D. So we showed that angle A is greater than angle C above angle B is greater than angle D here. So this completes the question that was given to us. I hope you enjoyed the session. Bye for now.