 Hello friends and welcome to another session on geometry and we are going to start new series on one very important topic in geometry and that is quadrilaterals So you must be aware what a quadrilateral is So we will start with deciphering or let's say breaking this word into its component or constituent words how the word quadrilateral has come about what does it mean and what kind of geometric figures we are referring to when we say the word quadrilateral and then based after understanding that we will be studying some features about quadrilaterals its properties and different theorems related to that so in the subsequent Sessions we are going to deal with all these features as well as the very important theorems Which are related to quadrilaterals now quadrilaterals are very important and very you know It's an integral part of all geometry and later on you will see that there is a huge Importance given to this particular topic and there's lots of uses as well, which you will see in your later Topics, which you will be taking in mathematics. So meet analytical geometry or any other Topic like vector algebra, you'll see the understanding of quadrilaterals and their properties would be very very Important so let's begin and we will begin by as we have already done many a times we will be now understanding what this word quadrilateral mean first of all and Then we'll start with the basic definitions around quadrilateral and then we'll go into its features So what is quadrilateral the word quadrilateral? So if you see quadrilateral is made up of two Basic words one is quad and this means for Right quad means for and the other one is lateral which means side Okay, so basically quadrilateral is a geometric Quadrilateral is a geometric figure Geometric figure so let me just rewrite it properly So geometric Geometric figure is it it quadrilateral is a geometric figure with with four Sides Okay, it's a so you can add few more Attributes to it. It is a closed figure Okay, and It has four Vertices Okay, which are non collinear So let's understand all of these so basically in a plane if you take four points one, let's say a Another point. Let's say B Then another point. Let's say C and one more. Let's say D. So four points such that no three of them no three of them Are collinear collinear means Three of them must not lie in the same line Okay, so no three of them are collinear. So collinear points for example Two points are always collinear three points may may not be collinear. So this is a collinear It is an example of collinear points all the points are lying on the same line But then here the condition is the three out of the four points must not be collinear Okay, so now if you join the points, let's say I joined A to B Then I'm joining B to C then C to D and finally D to A so this closed figures if you notice, what do we observe here one is closed It is a closed figure. So you must you must be wondering what is an open figure So this is an open figure, right? There are three sides, but they are open So one side is like that second side is like that and third one is like that Okay, but the fourth one doesn't exist or for that matter. This is also an open figure Okay, but what are you lateral will be having or it will be a closed figure with four laterals or We call it sides as well or sides and the sides are namely a B BC CD and DA these are the four sides, then there are four vertices So hence the word quad four right four four vertices what all a B C and D Okay, what all then we have four angles as well So many a times a quadrilateral is also called quadrangles Quadrangles just like triangles. We can call them as quadrangles meaning four angles Isn't it? So there are four angles. So four angles are also there. What all so angle a BC angle BC D angle CD a and finally angle D a Okay, so four angles are also there four sides are there four vertices are there So everything is four so ends this figure will be called a quadri Lateral There are there's one more Geometrical aspect of this particular type of figure and that's called a diagonal What is a diagonal? Right, so diagonal of a quadrilateral is nothing but if you join two opposite Vertices right so hence diagonals here are AC and BD is it fine AC and BD are the diagonal. So how many diagonals are there in our quadrilateral? Two types two diagonals are there now. There are a few more definitions. Let's understand those definitions as well So let me just draw a Quadrilateral first so you can see there could be a variety of quadrilateral drawn as well So let's say this also could be a track, you know, oh no this this kind of a figure for example This Is also a quadrilateral, isn't it? So we'll see what are the nomenclature around it But for the time being let's consider this quadrilateral and the quadrilateral is named after its vertices So a b cd is a quadrilateral. Okay, so a b CD is a quadrilateral now so if you see Angle a and angle C are opposite angles opposite Opposite angles right similarly angle B and angle D are opposite angles pair of opposite angles Right, they are opposite to each other right angle a is opposite to angle C angle B is opposite to angle B Okay, similarly, there will be adjacent angles adjacent Angles and you would observe there are four pair of adjacent angles what all one is Angle a and angle B adjacent means They will share they share a common side Common side, okay, so angle a and angle B. What is the common side common side is a b Then you can see angle B and angle C common side is BC then third pair is angle C and angle B and This is CD is the common side and the fourth pair is angle D and angle a and the common side is a D Okay, so four pairs of adjacent angles. So these are all definitions, please Remember them opposite angles adjacent angle. Similarly, we have Opposite sides right so how many pairs of opposite sides? two pairs opposite sides, so if you see a B a B and CD are the first pair and the second pair is a D and BC so Two pairs of opposite sides, how many pairs two pairs? Okay, similarly, we have adjacent sides as well. So adjacent adjacent Sides and how do we identify adjacent sides? They will share Share a common vertex Okay, common vertex. So if you see what all adjacent sides can you see from here? So a B and BC these are adjacent sides right pair number one and the common common vertex common Vertex is B clearly similarly second pair will be BC and CD and the common vertex is C third pair is CD and D a and the common vertex is D and the fourth one is D a and AB right and what are the common vertex convert X here is a so these are some definitions Around the vertex. So in this session, what did we learn? We learned about what is a quadrilateral and What are what is meant by vertices? What is what are laterals? What are sides? What are angles? Then we also call quadrilateral as quadriangles quadrangles and then we understood opposite angles Adjacent angles opposite sides Opposite side here. This is the opposite side and Adjacent side. This is what we learned in this introductory session on quadrilateral. So in the later Sessions, we'll be dealing with the properties of quadrilaterals. Thank you