 Hello friends welcome again to another session on quadrilateral and today in this session my objective is to discuss all the different types of Quadrilateral you are going to encounter In the coming two years now what I have done is I have just Made a table for your convenience so that the entire information regarding the Special type of quadrilaterals are with you at the same place in the same place, right? So Basically how to go about it so you have the first column where different types of Quadrilaterals have been mentioned then we have Put the information around sides angles dinals the area of the quadrilateral and a particular diagram of that Quadrilateral right so my recommendation would be whenever you are solving problems keep this Slide in front of you so that you know whenever you require any particular Information around any particular type of quadrilateral you should be able to fetch it easily While you solve problems after let's say 10 odd problems You have done on one particular type of quadrilateral all the properties would be by hearted by you Automatically so you don't need to Deliberately by heart it the best way is to solve as many problems as possible and automatically all the information Related to any particular quadrilateral will be by hearted by you So let's discuss all of these one by one and then in the subsequent sessions will be taking up problems on the same So the first type of quadrilateral we are discussing is trapezium. So what is a trapezium? So I will draw the diagram of Trapezium so this is our typical trapezium. Let me redraw it properly okay, so Yeah, so this is a trapezium now in this case it looks like first let me just Tell you about the properties of these Trapezium right so let's say a b c and D in the case of trapezium if you see only one pair of opposite sides are parallel about the side So these two sides are parallel and these two sides ad can be see ad and Bc are not parallel. So they are called non-parallel sides Okay, so this is a Trapezium now two pairs of adjacent angles are supplementary. So if you see angle d plus angle a is 180 similarly angle b plus angle c is 180. So angle a Plus angle d is 180 degrees Angle b plus angle c is 180 degrees. So they are supplementary. Okay, and how to find out the area. So let's say the area will be Denoting it by the symbol delta is equal to half into Parallel sides some so a b plus cd Into the height or distance between the two sides. So height in this case is this height Distance between the two parallel sides. Okay. So this is the area. Okay, so this is typical trapezium now Let's say what is isosceles trapezium. So now in this the same diagram if if if ad is equal to bc So if a trapezium is having non-parallel sides as equal so ad is equal to bc then Then a bcd becomes a bcd is Or is an isosceles isosceles trapezium. So this is about The trapezium next let's move on to parallelogram. Okay. Now. What's up parallelogram? So if you see parallelogram as Is mentioned first of all it's a trapeze. It's a Quadratl, let me name this as a b c D a bcd are the sides opposite sides are equal and parallel so a b and cd are parallel first of all And they are equal as well. So a b is equal to cd Okay, now Similarly ad and bc are parallel so two arrows so arrows similar type of arrows depict that they are parallel lines and We say ad is equal to bc Right ad. This is ad is equal to bc and what all a b is parallel to cd as well ad Parallel to bc now if you see only one criteria is good enough So a b is equal to cd and a b is parallel to cd if these two are fulfilled you can say the quadrilateral is a Parallelogram similarly if ad is equal to bc and ad is parallel to bc then also It's a parallelogram. We'll see the proofs in the subsequent sessions. Okay. So this is a parallelogram. Please remember now Parallelograms have equal diagonals. So Sorry Parallelograms are parallelograms by diagonals bisect each other. They are not equal But they bisect each other. So that means if it is o so Do is equal to ob and AO is equal to OC Okay, so if you see here they have Diagnose bisect each other Okay, and What is the area? area is The base let's say DC is the base. So area would be Area is DC. So I'm representing is by Delta area is DC into The height between or the distance between the other two parallel sites or DC So hence parallels if you see you have a drop-up of pendicular From B on to DC. So let's say this height is H. So DC into H Okay, similarly, if you see since DC is equal to AB, so it can be said written as AB into H and Now let's say if you drop a perpendicular from B on to ad. This is ad Drop-up of pendicular like that Okay, let's say this perpendicular is H one. Okay. So hence area is also equal to ad into H one so ad is the base H one is the perpendicular and or BC into H one because ad is equal to BC. So this is how you can find out the area of the Parallelogram it's mentioned here Right now, let's see Rhombus so what is a Rhombus if you can see Rhombus is parallelogram with equal size. It's mentioned So all the sides are equal and obviously the it is a parallelogram. So opposite sides are parallel Right. So opposite angles are equal as well. So for example, this angle is equal to this angle So let me name it a B C D first criteria is ABCD is a parallelogram then AB is equal to BC is equal to CD is equal to DA and Angle A is equal to angle C and angle B is equal to angle B and What about diagonals diagonals bisect each other at right angle, right? Mind you they are not equal So Diagonals are not equal. Let's say this is O. So this will be 90 degree Okay, and AO is equal to OC and OD is equal to OB Okay, so this is what is about Rhombus. What about rectangle? So rectangle is again if you see rectangle is before that. What is the? area of Rhombus since Rhombus is also a parallelogram. So you can apply base into height there as well base into height and Another way of finding area is half into D1 into D2 where a D1 is equal to one diagonal So let's say D1 is equal to AC and D2 is the other diagonal BD Is it fine? So this is how you find out area of Rhombus. We are not going into the proofs in this session We will take up proves one by one later. Okay now Rectangle, so what is rectangle? So if you see a rectangle is let me draw the rectangle. So this is a rectangle rectangle Okay ABCD is a rectangle. You are already familiar with such geometric figures. So what is it? Opposite sides are equal and parallel. So AB is parallel. So it's a parallelogram in the first place and then Thus there are some special characteristics and that is each of the interior angle is 90 degree a Parallogram even one angle is 90 degree all other angles will have to be 90 degrees. We'll see how so all angles are 90 degree and diagonals are equal diagonals Diagonals are equal Okay, so if you see AC is equal to BD diagonals are equal Okay, and They do not Bissected right angles they bisect each other but They do not bisect at right angle. So that means this is oh, so if you see Again OD is equal to OB and AO is equal to OC. Okay, but they do not bisect at right angle. So please be very very Careful now you have already known. So let's say this is B and this is L then area Which is denoted by delta is L into B. So this is the Relationship for area of the rectangle and the figure you can see it resembles here this figure. What's a square guys? So square is nothing but again a rhombus with internal angle to be equal to 90 degrees. So if I have to just make a Squire so this is a square Yeah, this is a square where this is a D See D. It's basically a rhombus I rhombus because all sides are equal and Opposite sides are parallel. So rhombus with AB is equal to BC is equal to CD is equal to DA So how different it is from rhombus is that there's a special type of rhombus where internal angles are 90 degrees So some property matches with rectangle as well. So internal angles are 90 degrees So you can write angle B is equal to angle C is equal to angle B is equal to angle a is equal to 90 degrees Okay, this is a and Best part is diagonals not only bisect each other. They bisect each other at Right angle. So let me just draw a proper. Yeah, so from A to B. Let's say this is a diagonal so hence diagonals diagonals bisect Each other at Right angles Okay, and I know sir Equal as well. Okay. All are 90 degree, right? So most ideal Quadrilateral you can see you can say it is the most ideal quadri Now what about kite? So let us draw a kite. Yes guys. So this is kite a B C and D so if you see in this kite, so let me write it kite In kite AB is equal to AD so two pairs of Adjacent sides are equal CD is equal to CD is equal to CB and What else if you see angle a DC is equal to angle a BC using congruence you can easily prove it and The larger diagonal AC AC bisects smaller diagonal BD at Right angles Okay, so this side will be equal to this side. Let it be o and this is 90 degree Okay, this is all about Kite, okay. What else area area of the kite is given by half into D1 into D2 again. What is D1 the longer diagonal? D2 is the smaller diagonal. Okay, half into D1 into D2 using the formula half into base into height you can easily Find or prove this particular formula. So this is all about Different types of quadrilateral guys. So what I would suggest is you keep this slide In front of you whenever you are trying to solve the problem. So I'm just so you can take a screen grab of this as well. So This is the slide which I want you to keep In front of you whenever you are Trying to solve problems you do quadrilateral in the subsequent session. Let us take up problems on quadrilateral and using these properties will try to Prove or let's say, you know achieve the desired result in those problems. Thank you