 Welcome friends to another Theorem in parallelogram and this theorem says that in a parallelogram opposite angles are equal Okay, so we are going to prove this statement Yep, so let's begin. So what is given if you see? it's given that ABCD is a parallelogram. So hence I can say AB is parallel to CD and and AD is parallel to BC these two things are given and you have to prove to prove That angle A is equal to angle C and Angle B is equal to angle D Now what approach should we take there are multiple methods you can do actually you can Join the diagonal DB Like that and then try proving congruence and then you can do like that or the easier method would be Let's use the properties of parallel lines. So if you see AB is parallel to CD, isn't it? AB is parallel to CD. That means AB is a transversal Sorry AD is a transversal AD is a transversal, isn't it? Okay, that means what angle A plus angle D must be equal to 180 degrees why co-interior angles Co-interior angles co-interior angles are supplementary in parallel lines Co-interior angles on a transversal on a transversal To parallel lines parallel lines are supplementary Are supplementary this is the Basic reason behind it. So A plus D is 180 degrees similarly you can say similarly Simi Lerly similarly since since AD is parallel to BC as well Therefore Angle A plus angle B will be equal to 180 degrees Okay right, so if you see From Let's say here. This can be written as angle D is equal to angle 180 degrees minus angle A and Here angle B is equal to 180 degrees minus Angle A. So let's say this is two This is one So from one into what do we say see from One and two to Angle D will be equal to angle B because both the RHS are same so angle D is equal to B So opposite angle angle B is equal to angle D and with the same logic You can prove angle A is equal to angle C. Yeah, so same logic you can apply and You can prove that Angle A is equal to angle C in this case you should have taken Angle C plus angle D is Equal to 180 degrees right now AD is Parallel to BC for the second case. What will you say you will say angle C? Plus angle D is 180 degrees. This is also true. Let it be three Okay, and here from here you can write angle C is equal to 180 degrees minus angle D and if you see from here as well, you can have Angle D is equal to sorry angle A is equal to 180 degrees minus angle D So this could be four four So from so I'm just writing it here from three and four Right, you can say angle A is equal to angle C. So this is also proved isn't it? So this is how you have to Go about this proof. So hence, please remember this theorem. This is also very very important theorem