 Hello and welcome to another session on triangles So we have yet another theorem and we would try to prove this theorem in this session The theorem says the line joining the midpoints of two sides of a triangle is parallel to the third side Right this theorem you have studied in previous grade as well, which is also known as midpoint theorem But we are going to use and sorry prove this using Basic proportionality theorem and converse of it in the last grade that is the previous grade You have studied this if you have done this proof using congruence of triangles So let's now see how we can prove this using basic proportionality theorem. So the first thing is let's draw a diagram So here is a triangle. Let us name this a b c a b and C a b c right Now let's say point D is the midpoint of a b and point E is the midpoint of AC and let us Join this Okay, so I've joined D e we have to prove that D e is parallel to BC Okay, so let's prove this. So what is given? Given is D and e are are midpoints midpoints of a b and AC respectively Okay, what is to be proven? So D and E are the midpoints of a b and a c respectively. You have to prove that D e is parallel to BC So let's write that so to prove D e is parallel to BC, okay So how to go about it? So see in this question or in this theorem There is something which is to be proved as parallel to the other side. So Basic proportionality theorem, you know can be useful and since we are trying to prove that something is parallel to something in a Triangle two sides are parallel in a triangle. So converse of B P T is going to be very very useful So let's try to prove this now What is a a d d any other midpoint so you can say a d by db is equal to 1 Because d is the midpoint and similarly a e by e c is equal to 1 because of the midpoint right therefore You can say a d by db is equal to a e by e c Right a d by db is equal to a e by e c right now by converse of Converse of What basic proportionality theorem, which is also called as Thales theorem. So by converse of V P T we can say that D e is parallel to BC right what was Converse of Thales theorem converse of Thales theorem suggest that if you have a triangle Okay, and there is a line parallel to or Converse of the theorem says that if there's a line which divides the triangle Let's say P Q R is the triangle and it divides In such a way that PS by S Q is equal to P T by T R then Then what will happen ST will be parallel to QR. This is what is converse of B P T using this converse of B P T. We could establish this given theorem