 Now, let's deal with theorem number two. So in the in the previous theorem We saw that a diagonal divides a parallelogram into two congruent triangles Now we are going to use that property to prove that in a parallelogram opposite sides are equal How to go about it? Okay, so let's Start the proof using the congruence. So how to do it? So we have joined a diagonal BD Okay, and let's use this So as we have done all already will write given abcd is a Parallelogram Okay to prove what is to prove? What is to be proved? So you have to prove that? a b is equal to cd and ad is Equal to bc correct. So a b is equal to cd and ad is equal to bc Let's do that. So whenever you see such kind of for, you know, you Let's say if you have to prove two sides to be equal So one way is to prove that they are part of their corresponding parts of congruent triangles CPCT and hence We are done. So let's try to prove that. So prove is very simple What you need to do is you have to take in triangle in Triangle a bd and triangle C db So if you didn't notice, I'm just trying to write the triangles where corresponding parts are equal So a must be equal to C b must be equal to D and D must be equal to be like like that So please be very very careful while you are writing The congruent triangles, right now in triangle a bd. What can I say? I can say angle a B D is equal to angle C D why they are alternate interior Angles why because a b is parallel to cd because it's a parallelogram Similarly or the next bd. So bd side is equal to db side Right. Why they are common common side common side Okay, and third one angle a db is equal to Angle C B D y again alternate interior Angles alternate interior Angles right and what are the parallel sides ad is parallel to bc because of the property of the parallelogram therefore Tell me which criteria of congruence did you just use it is nothing but angle side angle a s a therefore by a say a s a congruence criteria By a s a congruence criteria triangle a db is congruent to triangle C D Sorry triangle a bd not so hence. I was making the same mistakes. You have to be very very careful a bd is congruent to C db. Okay. Now what? therefore a b if you see a b must be equal to C d Why you can write corresponding parts of Corresponding triangles, sorry congruent triangles, right? similarly See me l early What can you say? Ad so if you see this is ad ad must be equal to cd cb that means Proved, so we just proved that Opposite sides of a quadrilateral sorry parallelogram are equal. It's very very important theorem So please keep this theorem in mind We will be using this multiple number of times in problem solving