Transcript for:
Euclid's Geometry Overview

Yes, hello everyone, this is late. In today's video, we are going to talk about In today's lecture, we are going to talk about Chapter number five of your class ninth Introduction to Euclid's Geometry about a very easy very cute This is a very small chapter which we call a joke. I will complete it jokingly and you will say Wow, brother, all the questions are from me. If we are going on then with this energy, Let's start today's lecture with enthusiasm. I understand I understand There is one thing, one thing I don't need less than you I want to talk to you personally about this chapter. I haven't seen many comments about I saw it in the video brother that Bhaiya next chapter Euclid Geometry next Chapter Euclid Geometry then came to my mind It is such an easy chapter in it, why children I am so demanding youtube2 People have created a website on geometry. Have you prepared the lecture or not? All the people have made it, then I said Friend, even though so many people have made it If children are facing problems then the reason behind it is What is the reason for this? Then I came to know when I saw all the lectures inside that either people They have shortened it in a very easy way. After doing it, he told me that those people who gave him half the money It was done in half an hour, it was just a joke. I've seen it happening in Only and only they are cooked from the top. I am telling you if any questions come to you. Then some people will not be able to move who also asked questions What have they done with bookish language? I got the questions written on the surface only. The answers have also been given in Hawa Hawa. You don't know what the exam will be about You should also know that you will come after writing People have also got NCERT solved. He also wrote the NCERT language. He also simply wrote that Look, write it like this, write it like this, write it like this You will have to pay, brother, how will you write it in the paper? So now I understand this chapter. I am coming, why is there so much demand? Because children do not know that the exam How should I write it logically brother? It is correct, I understand it, but How will you write the exam today? I am going to tell you in the video, watch this For the video, I thought at first I too I will teach you in half an hour, then I I thought friend, I have to teach you in a good way. It has to be taught in such a way that after this the child Do not go to the next lecture, after this the child If you can solve one question then in between All the solutions that I have written in I will get you the entire NCERT solved, Bookish I will not get it solved in language here. All the solutions, even if typed, But I have typed this in my own language I am typing in Type in this language I do that just by looking at you You will understand that yes friend brother, how much It is an easy thing, so I kept everything in my It is very cute to type in the language I will teach you the right way, just have faith and start. Watch the lecture from beginning to end Watch the video till 8 and you will get this The chapter will appear to be ending It will be known that you are sitting with this M In class ninth, I said, "Whatever M is, that's mine." 100/1 in maths, we both together I will complete the remaining chapters. If the lectures are already on the channel then If you feel like it, you can go and see that too. You can complete it first. Look my love Euclid Euclid was a mathematician who This chapter is very short in time, isn't it? The chapter is instant, meaning very early. Meaning, where people also understand the meaning of points. I didn't know where people had to line up. I did not even know the meaning of that definition today. In the chapter we will read about Euclid who was He was a mathematician of that ancient time. who wrote all these definitions, meaning You understand that this was our Baba. who at a time when people did not even know what geometry was when people knew I also did not know what a point is, what a line is. At that time he had calculated the entire geometry. I told you a few things about the same We will read some things in this chapter today. If they are there then basically we are paying tribute to them. friend, whatever things you have given You had read whatever prediction you made at that time. Curry prediction will say no no no All the things you wrote at that time. If things are going well today, think about them. Today we are going to study, okay, so basically In this chapter we will discuss very basic Euclid Baba will read some things I will read the things I told you, okay, do you understand? Let's start with the first thing that Euclid Baba told Euclid something The definition was given by Euclid, who was a Baba. Give some definitions, this definition is very Logically correct, you will say brother, there is something there too. No, but understand that this is about a time when people I didn't even know, so we had to understand all this. We will have to remember all this This is a chapter about theorizing but it is remembered like this. I will get it done so that it will be fun, the first thing A point is that which has no part meaning Bhaiya, this is a point, point one, so small It is such a small thing that we And parts cannot do this first definition So if someone asks you about the point what is the definition so is the definition of point The point is something which has no part to understand This is what you said in the entire chapter. What are you teaching me brother? There is a line definition line throughout the chapter What does the line is a breathless length mean? Meaning this is a line, what happens to it There is always a length, what is this length? We also write that one of this line If you don't write breads then it's basically a line. what is the definition of if someone asks you If you ask what is the definition of line then line The definition of line is a breathless length This entire PPT is for you Just look carefully and open your ears. I have to listen to the third definition after that. What he gave was that whoever is at the end of the line There are points, those are points, meaning You will say, brother, what joke are you telling? This is my love, the end of the line Points means this line which was there This is the end, this is the end, and this is the end, what is this? Points are basically and in easy language If I tell you in language and in simple language then one A line is made up of points. There are many points one after the other. one after another one after one after one one after another one after one after one one after another connected like this There are many such connected The points got added up and thus, they got added up. What did they make with this joining together? I made a line and at the end also a There will be a point in the beginning and there will also be a point in the middle I will also have a lot of points, this is it The third definition that he gave is The ends of the line are points on a straight line line is a line which lies evenly with the Points on it self, this is what I just talked about Told that there are many points which are very All the points, which is a lot of points What do all these things combine to form? A line is formed, this is our fourth Definition: So, what is the definition of the first point? If I ask you for a point, what will be the point? Meaning, which has no part, line meaning A breathless length means just its length no breath no breath no breath Only length is length, the third one is of the line There are ends, those points are the fourth The points meet to form a line Fifth, a surface is that which has length and Breath only surface surface someone like this Surface okay this is a surface that has a length And it will have one breath, this is the fifth one. Point is said to be a surface which is Not like this podium is placed here. Let me pick this up and show you where this podium is placed. So it has some surface and it has some length. It has some breath, so this is the surface. There's a surface, okay, it's a plane surface, then After this, if I talk about the fifth point You got it, come on, come on Ja yes then after that sixth point the edges off surface r line like these points these points This becomes a line, this point, this point, this one The line is formed, it becomes a line, so these edges what are these edges what are these lines Whatever surface you take, there is one like this There will be a surface, so there will be a line in it too. one this line one this line one this line one this line one this line one this line one this line so What are all the edges of the surface? The lines are very basic. I don't want to make things funny but you should understand. You will have to remember because of this The chapter is above, now it is there so you have to read it. Now a plane surface is a surface, any one A plane surface is a surface that has There are a lot of straight lines, brother. Look, this is a surface, there are many strata on it. The lines can be like this, like this, like this, like this What are the many straight lines on this? This is our seventh point clear clear back quickly Revise, we will proceed first while revising what is a point what is a point What is a line that has no parts? Which has no braids, two points Done, then what about the end of the line? There are points, there are lots of points What happens when they meet, a line is formed Four points are done, then a surface after that. What is the length and breath of a surface? What are the edges of a surface? What are lines? This is the fifth and sixth point and By drawing lots of straight lines on the surface Maybe this is our last point. Here are some definitions of Euclid's that we remember: I have to keep it, okay, okay, now it comes after this. a thing called a thing called Universal Truth What I said now is a There comes a thing called universal truth. Universal truth means something that is always Truth is universal truth, meaning it is everywhere. It's true, I have a pen in my hand. It is a universal truth because yes it is visible There is a beautiful thing in this world A boy named Nirvana lives here. This is a universal truth, yes I live like this I'm recording this at the time. Universal The truth is, I am giving you this lecture right now. Universal truth is somewhere If anyone asks you anywhere, tell them. You can, yes I am seeing it, so basically Universal truth means that which is in one world The truth is called universal truth. So our brother Euclid was Euclid Bhai Saheb was the one who taught this universal truth He made two parts of it universal. Truth is in two parts, one is We say Aegium is what we call The Pochle one we call Aegium one we call It is said that pochale aegym means aegym means that Truth that can be found anywhere in mathematics can be used what did i say said I didn't have every where every where in Mathematics Everywhere in Mathematics Like Truth that you can find anywhere in mathematics You can use it anywhere Ho pochale means such truth that you who You can use it in geometry only. in Geometry Geometry and Geometry Box No my love, not the geometry box Geometry does not mean what is drawn between lines Vines, angles, angles, all that is Euclid brother. Sir divided the universal truth into two parts. Each part which you can see somewhere in maths You can also use geometry or algebra. be anywhere and there is a part which is just And this is only limited to geometry. There is universal truth and its two parts So if someone asks you whether Aegium and Tell me what is the difference between the two Will you give me Easy PG, is it Aegium, meaning somewhere? You can also use those truth and pochale Meaning, which is limited only to geometry. If we look at it in English, So the British used this language in this way. What are the axioms and pochle Euclid sem Certainly now you see what I have done to you He told the British in a very simple way How much more difficult did it make it? Made it more difficult then Bharat Mata Ok So Jai also say yes then Aegyum and Look at me Meditation Euclid assumed something Properties that were not proven, brother There is no need to prove universal truth. This is a pen in my hand, prove it. If there is any need to do so, what did they Get some properties which need to be proved There was no need for these parts are called universe Truth is obvious, universal truth is obvious. vice is universal truth then some Properties that do not require proof What do we call them, universal truths? It is said that they divided them into two types Accounts of Aegyum and Pochle He divided it and used the term Pochle for the part that was specific to Geometry and the fraction used through out the Mathematics on the other hand, the umpteenth use through Out the mathematics anywhere you use it You can tell him what we call him They say Aegius means only geometry is limited to and eximous means which you You can use it anywhere in mathematics. This is the definition of Exims and Poch now. Some we will read aegypt, some we will pochalesup You can also use it and pochale means whatever If you can use it in geometry then first We'll read some Aegyptiaca, then we'll read some we will read five okay okay so till now we What you read, don't take it too heavy, don't load your mind Don't take the load, read very easy things from this What did we read before? Before we just Read what Euclid had said Definition di, if this definition is clear then These are some definitions followed by some exempla and then read some more This is the end of the chapter, just some definitions have been given. Euclid Bhai Saheb said something Exims have told something they have said Tell me, if we read only this then we have read the definition Lee now reads Aegium so Aegium What all has Euclid Baba given us? Let us understand the principles given by Euclid. We understand that first thing which we will see Very very means so logically correct Whatever you say, brother, is it a big deal? It is not there and it is written here, so pay attention You should understand this axiom from here. Definitions should be remembered by numbers. Whether you remember it or not, it doesn't matter, this Aegium You should remember from the number that the first The number aegium is Euclid's second number Aegium This is Euclid's third number Aegium that's it okay once twice three times 10 If you write it once, you will remember it. First understand the first thing. things which are equal to the same thing are Equal to one inside, see what I said I will explain it with a very good example, a a is equal to b and a is equal to c is equal then it implies that b And c is also equal to this, this is the first thing that happens. Things which are equal to the same thing b also a If a is equal to c then b and c are also equal to a The first point has said that they are equal to each other. is b also equal to a things which are equal to the same thing then b is also equal to a If c is also equal to a then b and c are also equal to each other equals these things which he said are equal to the same thing are equal to one another So equal to one inside is also there, this is the first one. aegium second aegium if equals are added to Equal the holes are equal what did you say If a equals b, add it to both sides. I am adding edging to both sides If the same quantity is added on both sides then a p 2 and b p 2 what will these be will be equal, this is our second axiom What if equals are added equals means two give equal thing and give two things if you both Even if space is added, there is no harm to the equation. The equation will remain the same if a and b are equal and on both sides we have some I also added anything, meaning anything, the same thing. Add x to both sides and add y to both sides. two on either side two on either side four on either side five on both sides six on both sides 10 on both sides Haj 2000 Add 10 crores on both sides if Add the same thing on both sides because it It is being cut, if it is cut from two then it is cut from two. If you are adding the same thing to your For convenience, there is no loss on that equation. These will not reach the Second Age I said equals are subcut from equals such that A equals B and Substitute to both sides If subcut, then a-2 and b-2 are same on both sides Even if you subdivide things, they will remain equal. This is it. Our third axiom is na, PG fourth aegium things ch ch coside things ch ch coside with one another are equal to one another what He said that the fourth side means one Suppose there is a line above A and a line cd9 kar hi hai ko inside kar hi hai meaning It is stuck right on top of it, so both of them If you have said exactly this then it will be equal things which coincide with one another Who is doing it on the other and is stuck is stuck exactly evenly so it What will both be equal, this fourth The point is the fifth point, understand the fifth point. The whole is greater than the part means look The Whole is Greater Than the Part this is a whole pizza okay this We have a whole pizza out of this. If you look at one part, let's say this There is a small part, we did not remove it. I took a separate part which belongs to this one, assume it. We took out a part from this and then Even if it is filled, it is a hole and this is a If there is a part then whatever is the whole will always be a part. He has said that it will be bigger than brother one We have a whole globe and in that there is one India. So if I take only India, then it is empty India and the entire globe The globe, which is our entire world, Yes, it will always be bigger, so the hole is It must be bigger than an empty one. He said the fifth point, whole is greater then the part so if we take the whole pizza Take a blank and compare it to a part So the hole will always be bigger, okay? Sixth Point: Things Which Are Double of the Same thing are equal to one another things which are double of the same thing like say, say I have a friend named Ram. I am Ram to Ram, let's say his weight is 40. I am double the size of Ram, which means I am 80, I have one And there is a friend who is also double the size of Ram, so he too If it is 80 then both of us will be equal, this is a bo Point you will say brother friend this is a joke This is what we came to see, life, I mean, a logical thing. But the children are confused by its questions. Let us go through its NCERT questions. If the children do not understand it then It might take a bit of a headache, but I'll tell you. Look what he said, that double of the same thing. I am also double of this thing, this is also double of it If so, what will we both be to each other? He has said that things will be equal. which are half of the same thing, suppose its weight My weight is 80 and I am half of that. And I have a friend whose weight is 40, he too If this is half of this, then this is also half of this and I am also Half of this, we will also be equal, so things which are half of the same thing, both its halves I am half of this and we are the other half. He said that both will be equal. At seven points, you should understand the sixth and seventh also. These are Euclid's axioms We should remember this by number. If you want to remember by number then the first number is What Axium Says Number One Axium says things which are equal to the same Things are equal to one another, these first A also B that b is also equal to a and c is also equal to a, so b And c equals this first then after that if Equals are added to equals this second a It is ideal if the same thing is added on both sides. Even if two there is no problem, the third one says Even if you serve the same thing on both sides, no one No problem, the fourth one says that if one If one sticks on top, that bean will be the fifth. It is said that the hole will be bigger by one part. The sixth one says that if I I am double and she is also double, so both of us They will be equal, I am also half of the same thing. If that is also half then both of us will be equal. We have seven axioms. Take Euclid's. If you want to take a screenshot, then take it. Take a screenshot or do it again Write lightly because on it We will ask you some questions now. So you can't remember it, that's why Let me write this down lightly that the first This one used to say, second one this, third one this, now when you If you ask questions, you will understand. Let's ask some questions, look at AIIMS. My love, did you understand? Did you understand? First equals two. Same thing equal to one another equal add No problem, equal subcut, no one No problem, one stuck on top of the other The hole will be bigger and double in size. It will also be the same, which is half of the same thing. They will also be the same, these are seven packets. seven ageum let's say the first question a is of the same A as B. What A is is of the same B. age of c is of same age of b c which is He is also of the same age as B. Who is Euclid's Sa Aegium is between A and C The relation tells us that brother B is also equal to A. A is also equal to B and C is also equal to B. From here we can say that A and C are also equal to things which are equal to the same thing are equal to one another which one piece which one aegium which aegium which aegium says Things Which Are Equal to the Same Thing First Axium Answer Will Be First Axium This Is it Now he has said it is known that x pwa which is That is equal to 10 and I said x p z = 10+ h is if same thing is added on both sides Equals are added to the same thing if equals are added to both sides so the whole thing is equal Which P axium is this, which axium If the second number is axiom then the answer will be seconds Axium third section comes on look one You have given us this figure, this A B CD. There is a line given on which there is A B CD. If a equals bd what has given us if a If whatever you have is equal to a BIDI then prove it. I have to prove that it is equally rotten, okay? what have you given us, you have given us this and What proof do we need if this BIDI is equal? What I have to do is that whatever is there is equal to roti. to understand carefully to understand something carefully What did he say, he has given the entire line. It says that A and B are equal proof. What do we have to do with the proof holder? We have to write proof that A and S Equal How will we do this, these have been given equal importance. What is one thing common in both? That is, there is one thing common in both of them. What is happening is this, remove this common thing If you give it then Subbox Cutting from both sides And from Axium number three from Axium Number three, we know if equals complete. Write here if equals are subadmin If it is also equal then write it completely here. okay give it, I will tell you in the exam I am trying to learn how to write so subks both Sides, which enzyme did we use? If we look at both sides of the bcc950 So a left If bdc2 or bc4 is entered then cd-dvd Let's move ahead, it is known that, hey, this is This is the same question, it is the same question now. So the next question was asked by Ram and Ravi. If you have the same weight, then consider the weight of Ram. That is x kg and Ravi, hey, both of them If it is from R then Ram and Ravi both have Both are x kg, okay, so we have Ram The weight of is given to be equal to the weight of Ravi. If each one gains weight by 2 kg, both of them What did Ram do, Ravi also added 2 kg also added 2 kg how will there New weights can be compared on both sides. The Dodo has been added to If Equals Are Dead Too Write equal axiom number two, what is this? From azium number to if equals are added to equal then the resulting will also be Equal, so whatever weight they will have later, that too Equal will happen then the resulting weight will Also be equal, you will write it as easy PG, understand I just have to write what Ekam number two says. is equal to equal then the resulting will be equal there for their final weight will also Be equal, we have to write this, okay, this I am asking very simple questions. I am not getting it written in this, you should write it. You will also get a little brain damage from NCERT. If we understand what happens to children, we will We have read the definitions, now we will read the axioms. Some read Pochle Pochle means Polet Meaning that is limited to geometry. Obvious Universal Truth Universal Truth Limited to Geometry Limited to Geometry which is what do we call them what do we call them We call them Pochale, this is also there Nothing is easy, you will understand it when you see it. The name is postulating To any other point this pochle number one hai whether between one point and another We can draw a straight line in The first pochle is one point and the second point We can draw a straight line in the middle. One of its principles is called To Distinct Point there is only one unique line brother You can draw a line from both points. This is a point, this is a point, so a line It has also become clear that this will be the only line. There will be no other line apart from this. There is always only one distance between two points. There will be a line brother, what else can you make, this one There is a line brother, these two have been connected like this. Look, brother, by doing this, this is someone's line. What is a line? Give a straight line. There will be a line between the points and that There will be a unique line between two points There will be only one line, only one The unique line is passing through those two points Only one unique line will go between this says pochle one and assim 5.1 pochle number Two pochle number two says terminated line can be produced indefinitely in this one line How far can we take this here? How far can one go here? No problem, says Pachale number two We know the line here is also infinity. It can go, Infinity can go here too. No problem, what does Politan Three say? This circle can be drawn with any center and Any radius I took a center this radius Let the center be a point and the radius a line If there is a segment, I can make a circle from it also. I can't I, I admit it a little bit Radius LU will also make a circle and smaller If I take this, it will also make a circle. I draw a circle with a center and a radius. From one center and one radius I can draw a circle He has said that he can make it. This is a basic thing, so you understand it. Gai Pochale Number Three Pochale Number Four All Right angles are equal to means what a joke I did not say anything, everything was right angle. They will be equal to each other, all right If the angles are 90 degrees then all are perpendicular to each other. They will be equal, that is what right angle means If it is 90 degrees then all are 90 degrees So all will be equal to each other, they are very These are funny things but this is from that time. It's time people knew about these It was not even there at that time Postlateral Polet Number Five, what is that? says if a straight line falling on the two Straight line make the interior angle on the Same side of triangle taken together less than If you don't understand the angle, I will tell you. Yes, look, I will explain the fifth number in the paper. What is this little brainy pochle They are not even intelligent, that means the British It is written in big lines, now see How will I explain Hindustani to you? Look what number five says. What does number five say my love Patcht number Five says let's say there are two lines, one line is this l is a line is this a okay and Suppose one is transversal okay one is a transversal then two lines form a transversal This angle will be formed and this angle will be formed. One and two will make one this angle and one this angle. It will become three or four, he said, brother, he is going. What did we call these interior angles? They used to say 1 2 3 4 what is the interior angle What is one and two interior angles on the same side of transversal this side has three and What is four on this side on the same side of Transversal is saying that the interior The angle on the same side of the transversal is Take the sum, like one and two are the same. It is on the side and three and four which is one on the same side If so, listen carefully to what is being said. Two lines are transversal and one is same. Take the sum of the side angles and this interior angle On the same side of the transversal, take their sum. Took this interior angle on the same side of Transversal sums of these are taken whose sum is less The sum of the days will be 180. Whatever line is there on the side, you will find it at the back. The line on this side will go back. You will meet at one point, what did you say about it? what have you said about this, this is what you said about this Pochle Number It is five, isn't it easy, isn't it easy, so I said this go It is being said that if there are two lines, then the interior Angle on Same Side of Transversal Ye Interior angle on the same side of the transversal This is also an interior angle on the same side, right This is the side, this is the left side, so both sides Take the sum of these two, I took the sum of these Took the sum of both, where the sum is less than It's 180, she'll go that way and meet me at the back. He said this line The postlateral line is falling on to straight Line Making the Interior Angle Taken Together Less than to right angle to right angle ka sum Meaning the sum of 9090 and the sum of 180 give the two Straight lines if produced indefinitely Meet at one side in which some is less than two Right angle where some is less than to right angle It will turn 180 and he will go back. You will find this in post number five. He said okay, so we read five pochals a lot. Easy is easy, nothing, one more time and back The first is between two points A line will be formed, that line will go very high here also. It can go very far there too. The second five and the third five can form a circle. Ho radius and fourth pochle from the center what that All right angles are equal fifth What I just told you Where the sum of the interior angles is less than 180 Go back there and you will find that line, this is it Your five pochal so I have given some definition Read them and need to remember them with such numbers Aegyptiaca is not to be remembered by numbering It is important to remember the numbering of the pot as well. We need Okay, so the theory ends here. If the theory ends here, then Not further, just a little more, just a little more There is a little bit more Look, there are some universal truths whose proof There is a theorem whose Proof is needed that requires proof What that requires is proof that it is known. Theorems, so theorem means such a statement Those who need proof that universal Truth was Aegyam was Pochale was in them I didn't need any proof, I had already said it. What was said in the definition of Aegium and Pochle My life was in the dish of aegypt and pouch let that assume certain properties which were not To be proven is okay, not to be proven So what did we call them, Aegium? Select statements that require proof what shall we say to them We will say that there are some theorems that we have You have studied lines and angles in circles, right? I have studied in the triangle, I have studied a lot We read the theorem that an angle which is equal of triangle is 180, this is a theorem Yes, isn't it, and we have also discussed some theorems in the ninth I have studied a lot in class and in circles. If you read a lot of theorems, you will They also need proof of that. We say the theorem okay so aegium polet Universal truths that need proof It is not a theorem meaning it needs proof If you are asked about the difference, You will tell me that I understood, I understood, let's move ahead. Your NCERT questions increase. If this is your NCERT question then this We have to prove this theorem Understand carefully, understand carefully a little It's just a smart thing, I mean smart. It is not very easy to write on either. Which is when something has to be written in the exam When the kids get shaken up I How do you write in the exam? I will tell you and also tell you how to think. So listen carefully to prove that to Distinct lines cannot have more than one Point In There are two lines in common, one is a line, say A. Assume the line is a is a line ok l is a line m bol Prove that both of these Those who will have more than one point in both There will not be any common point, only one point will be common. We know that whenever two lines will intersect, only one point will be common We know that he is talking to one person. There won't be many, we have to prove it. Absolutely no more than one common point If two are distinct, they are distinct Meaning there are different lines if you put them inside So there would have been many points but this is distinct two different lines two different lines Whatever is there is always at just one point This is the truth, this truth will intersect us I know we have to prove this to one another. There won't be much, what is wrong is what we need to do. Prove that there is not more than one If there are more than one, we have to prove it. The points that will be there will not be common. Let's prove this with Na Contra IX We assume there will be more than one value. Take p and q which are in l also have p and q which are He is also in m what did I tell us Proof that more than one point is common If not, I will assume that from one More points in common I have already said that there is p and q on l also. There is p and q on it too, I said this but Then I remembered brother, the number is lowered. Forest Postlateral number one's xGM is 5.1 says says that from two points only one The line will go but what I tried here In that, this L is also going from two points. There are two points, this m is also going, meaning What is my Ajman, if it is wrong then what happened? What I assumed was that from p and q, l also It will go from p and q to m, this is contradictory. Done, I had done both p and q. I will bring it on Contra became a contract with Pachunkar. Meaning what I was thinking and what I have is There are contradictions between people who are going wrong. It means what I thought was wrong I apologized, sorry sir, only one. The line will go, meaning there will be only one point. How can we express what is common in language? How will they write in their exams? I explained it, see how to write it. See if you have to write this way carefully. Listen to what I just told you written in English written in English Two distinct lines have been given to us by L and A so there are two lines one is L one is A to Prove L&A Can't Have More Than One If we have to prove this point in common then Given you will write that L and A are two distinct The line is distinct means distinct means There are two separate lines, not side by side. She is doing it okay, there could have been a condition If we commit suicide, many people would commit suicide. The points would have become common brother, this one line, this one The line is saying that many points are common. Yes, there is a distinct line, okay, so give it to me. There is a distinct line, both sides have to prove it. More than point common will not be proof if a and m are parallel then there is no point in Common of course brother, one is from one side. Another one is that a and m should not be parallel. So we said that A and m are parallel. The first point we have made is that this should not happen Wrote it okay so a is not parallel to m Let p and q be two points common to both Lines p and q are common to both. In me also L in me also L and A which are two lines Which is L line and M line, in both of them It is coming out like this while typing. Okay, so we said what's the late p and q b two points common to both lines a and m are common to both p and q, that is I said that's what I said about p and q In this also we have assumed p and q. Now we observe that line l contain both Point and line m also contain both point m I also has both points p and q in l Both points are but according to Postlateral one line passing through the two points there four l which is parallel to m will be If you understand what I am saying, then this is parallel. There will be a condition but it will not be parallel. Could have done that, that's what I said, A and A parallel It could not have happened, but if there are two points then Yeh there four yeay I wrote this line wrong Don't write this, don't write this, write this wrong This was not a parallel point at all I am getting confused, please understand from back. Understand that you have a little brain back. It is a question, meaning it takes brain to write it. There is nothing to understand, I have given two p and q. Point I agree, I agree that it is also in I. It is also in m, so I wrote we observe a also contains p and q m also contains p and So, from the two lines and two points on q Only one line can go to this number One says there for this contact our umpan That l a n ot r parallel their four emptions Is wrong there four to distinguish line can Do not have one point in common Cannot have more Then one point in common, this is what happened to us This is our complete completion. Proof OK I'm finding it hard I'm finding it hard It seems difficult, nothing is difficult No, you'll read it back once, right? So it will seem easy, just have to write this exam I think you understand when I was thinking when I was explaining to you When you realized that yes Brother, you are right on both L and M. There cannot be two points because two points Only one line can go through these two How is the line being constructed? Exactly what I was saying, we have to put it here I have written on it that once you read the PDF You will understand, let's move on We have read some stuff on NCERT. Five, we have read some definitions, we have read some Now that we have read it, let us look at the NCERT solutions. Okay, look carefully, look carefully important important important very We will also give important examples, okay? What does NCERT's example number one say? NCERT's example number one is my love It says if a b and c are three points what is on line and b lies between a and c I said a b and c are three points and a line Pe and B, which is somewhere in between these two It does okay so this is the line A S There is a line in the middle of it, B point la does prove that a p We have to prove that bc-c is equal to a. How should we think about this here? What should we think about? The way we see it is that a p b So this is a pair that is being formed, this is a This pair is being made on the side of AC. is doing coside on AC Meaning it is sticking on A brother, it is an AC. This is a + above this bc-c whatever it is, he is cosiding over it sticking to it and we know that What is the thing that keeps us inside each other? If it is equal then this pair A + bc-c is equal to a, that's it. Proof Bhaiya, what did you say, friend, then understand. Can't you tell me what to say, hey look a+ A+ If we join bc-c separately and make a pair then He's putting us inside the top of A. It's clear and we know bye which was aegium number aegium number four or It was four and not one that was on each other. what they do is they are equal No, it was not Aegium, it was Pochle Postulating It was Aegium, it was Exim, I am the one confused gone are these things which coside each The other was number four, absolutely correct. Things Which Coside on One Another Are Equal To One other so we will say this by aegypt number Four by Aegium Number Four by Aegium Number We will say four, we will say from ageum number four I will say A+ bc-c inside with a we can see clearly that pair A+ and we know that by Euclid Axiom Number Four Sage That The Thing Which Are Side with each other are equal to one another There are four A+ The pair bc-c should be inside above A. If it was happening then both the people who would go inside This will be equal to what we have said in Ageium number four. I had read this example number one, now let's come This is important in example number two. It is important to understand this carefully. It is important to be careful Understanding Prove That an Equilateral Triangle Exists can be constructed on any given line segment is a given line segment okay Let there be a given line segment A I am making it big, so a given line Let's say the segment is A, we have to prove that on this given line segment we have a Brother, you can make an equilateral triangle. Take the length of the equilateral triangle. The sides of the same length are Equilateral Triangles Call Us Proof To do that we have to draw an equilateral triangle. If you can construct it, then look at it. There is a way to prove it to you, my brother. How will it come to my mind? When we were children, we did not know how to teach I understood you from childhood I am here, you read it from me and you will understand. If you go then see there is a very easy way to do this. This is a strange way to do construction. Look at what we have to construct. just keep watching Stay once what will we do A to center will agree Let us take A as the radius and draw a circle. What did I say, I considered A to be the center. Let the radius be and draw a circle Given A as the center, let A be the radius and made a center circle first case this first What will we do with the case again? What will we do with it again? Second point second thing second thing black The second thing we'll do is to The center will consider Let us again consider A as the radius and draw a circle If we draw it then let B be the centre and A be the radius. Let B be the center and A the radius, so Let's take that compass now. Let's take this center by keeping it like this It happened and this radius came up to here and by doing this If you rotate it, consider b as the center and A as the center. If we consider the radius and rotate it, then this circle become I understood that I am not doing it with the compass right now. So it might look a little bigger or smaller But you understand what the red one is. what's the red one the red one the red one The first one is a center a radius and The one in black is the one in black is gonna be that second one that b is going to shut a Ko Radius Now this place is now this place is now This place is pink pink, yes now this place is pink Both circles are meeting from there both Join the line and from there join both the lines. Do it at whatever point you are getting it. If the point is C then join it from A also from B Please join this too, this is construction, okay So first of all we will write the construction which It is written here, look draw circle with center A radius a is another circle with center b and Radius A will be called the intersection point. and draw line segments a and bcc950 I remove the black one and leave the red one. Look at the circle, in the red circle, if I If I ask you what is A, then A is also a radius Yes brother, from the center to any point on the circle Join it, that is the radius from the center Join any point on the circle and If there is a radius then what is AC, AC radius so in the red circle What is AC radius in The radius of the red circle is I have come in AC radius red circle in a is also radius a is also radius then a And what will be A, it will be equal to Bha A also Radius a is also radius a and a are equal We have understood this first thing, now if we look at So the radius was equal to A. So we wrote okay now if we look now if we Look in the black circle, the black one Let's take the circle A equals A. Remember Is A equal to A? Remember this. A and A. we equalized because what both were Radius was now if we take the black circle So the red one was blown away by the black one. If you look at B Center If A is a point on the circle, we have A as well. Radius said I ask you what BC If so, what is BC from the center of the circle? The one who joins the point is also BC. radius is bc also what is b also a is the radius and a is also a radius then a a is the radius then a is also equal to bc a Equal to BC If so, then in the black circle A B C equals then a bcc950 This was Ekam, the first number Ekam was CH R Equal Two same things equal to one another so all three We have made all three sides equal or equilateral. This is a triangle, this is an equilateral triangle Got it, got it, so once we made a circle Took it and saw two radii equal to each other The line drawn and the radius seen in the circle Made them equal so both the radii If they are equal, what will happen to all three? That's what I had to prove, they would be equal. So let me draw this figure back here. but you understand figure figure figure figure figure figure figure Figure: Yes, this was our figure, so we did this I saw that if both of us If we look at the first circle If you look at the red one, then the empty red one So a and a are equal to a also radius and ac also radius then both radius both if radius then a and a We just saw this in the black one. What did we see on the second circle? What did we see, we saw the black one Look, now tell the red one to go and tell the black one Look, bc2 radius a also radius so If bc-c and a are both equal radii then If both are equal then A A is also equal to A A A bc-b radius yes then a a is also equal to a bcc950 equals so what is this this one If it is an equilateral triangle then what you I have to write in English what I have to write in First, it was construction, I understood it. Now write the proof of what I told you. Are you in a circle with a center? Radius is ac-ac is also equal to a then a is also equal to b a bcc950 sides are equal otherwise it is equilateral We have proved that it is a triangle, so whenever If you get a question like this then you You will prove this in some way, this is your example Number two is absolutely logical, isn't it? This is a strange question, I have to ask it like this. I understand that I will have to do it this way. You understood it, right? Just let's go. Next question: Let's move on to the exercise. Number 5.1 tells us that the first The question is true or false, so tell me what Is it true or false? Only one line can pass through a single point Only one line goes from a single point It can go, it can go, it can go Yes, she is also going to be Sati, yes, she is also going to be Sati, this is also going to be Sati It can go from a single point How many lines can go, so what is the first number? What is the first number, it is false, it is single Many lines can go from a point. Multiple lines can originate from a single point. There are infinite number of lines which can pass through to distinguish two different points Multiple lines can go through a point. No no no only one can go Pochale Pochle number one ka axiom to yeh falls The first one falls and the second one also Falls is saying in the second one Only one line goes between the infinitesimals. It may not happen like a terminated line can be produced indefinitely on both The sides are much further from here than here It is true brother, I am saying this. Are two circles equal or red? Equals Red Eye Red eye is a plural word If it was single then the radius would be red eye means two so talking about two so two If it is a circle then one center and one radius Circle drawn and of same radius to If another is made from it, what will happen to both of them? I will be equal, it is absolutely correct, it is true. It's easy PG, nothing is easy, it's simple Fifth in figure A equals This is Aegium itself which is terminated, isn't it? If it is also Aegium then you will write all this. Which is the thing that is easier, more on that I will not give time to something that is difficult I think you're out of your mind If it happens, we will give time to it like this question like this is the question what is the question He says listen carefully and asks questions. Give a definition for each of the following terms There are many terms in which the first parallel There are three or four more lines like this and the next one is the next one. If it is written in the slide, then every single thing We have to give a definition like parallel line If we have to give a definition then parallel What are lines? Parallel lines mean Lines lines do not intersect Intersect brother such a line which somewhere These are parallel lines that do not intersect. A line that keeps going straight lines that do not intersect are called parallel lines If so, we had to give a definition. I have given the definition, what did I say next, are you there? Another term that needs to be defined first is The chapter is about anti-time, so in anti-time If you go and tell someone that there is a line like this If it does not intersect anywhere then you have today From millions of years ago he went and told someone A line in front that does not intersect anywhere He will say oh brother oh brother what is the line What happens, brother, what is the intersect in this? There are some things that need to be defined It's important that people might not know What things do they have at that time? I did not know the line, so I mean this definition To write, you first need to read the line You will also have to tell the definition and that of intersect If I have to tell the definition also then this is its There is a definition but there is something else in this definition. There are small terms whose definitions are also If I have to tell you then there is a term in it, line. I just read the line meaning breathless length. We played Breathless Length Intersect Mean Intersect Mean Intersect means a point in common a point In common a point In common a point which It is common now one thing has come back to the point You will also have to define the point, that's it This loop is running to define the point as well. Ka point means The part which we Can't divide It is unwise, meaning first you did parallel What is the definition of line like in this? There are things you have to define. So define line and also define intersect Another thing I pointed out in Kara Intersect Let me define the point also, so this is what This is how we answer it If you write, I understood, I understood, then how? I will write this, see what a parallel line is. Parallel lies are the lies that do not intersect at Any point, now there are three things in this? Before defining parallel lines, we have First you will have to define the line as well. People wouldn't know, not even Intersect. You might know that people might not even know the point. So the definition of a line is written as a point. We wrote the definition and also intersected it. I have written the definition, this is it, it is just this much. Na Easy PG Chalo Next Next Next Let's do the next one, I am talking Define Perpendicular Line Perpendicular Line Meaning whatever happens between them, cut at 90° So perpendicular lines are the lines that Intersect at 90 degrees, what is so special about it? Things that people may not know You may not know the word for intersect. I am talking about mathematics, you tell me brother Are you at that, you might not even know this, study maths If you are not studying English then I will study Maths. perpendicular The lines are those lines which are at 90° intersect then intersect and 90° its If people do not know the definition then before Defining the Perpendicular Line We Need to Define lines These lines also define the word You will also have to define the word intersect. And you will have to define 90 degrees as well. What happens to the line if it falls? Breathless I know the length, intersect means common point. You also know that 90 degrees means right angle, so this If we define all three separately, then First we will write a main definition and then What are the words in it that People may not even know the definition. I don't know what words were in it. There were lines, I wrote the definition of line Intersect means I wrote its definition 90 The definition of a degree is a right angle. It happens that right angle is an English word. You already know that people look at the right angle. What will come to people's minds? It will come, if you understand then what Euclid says We read the definition in the first slide. You just have to write it down below, define it. The third thing to do is to segment the line. What is a segment, see, there are three things. There is one line, there is one ray and one There is a line A segment line is something that is Anyone can go here too Neither is its end point, both It is free from the side, meaning starting It is a point, not an end point, it would have been a line. There is no end beyond here, beyond here It's not a point, it means a starting point. There is a point, there is a starting point but there is no end. Point is also a line segment meaning end point Starting point is also the line segment meaning There is an end point and a starting point too. then the line segment is a part of the line A small part of a larger line I took this line, it was a very big line. took a small part from which It has a starting point as well as an end point. Line segment is called part of line Having starting and end point is known As a line segment, now what is there in it I line one word came point one word came this We have to define so before Defining Line Segments We Need to Define Line and point to line hota hai breathless length and point of which any part It doesn't happen to you, easy PG, right? You will get the PDF and you will understand the radius of The circle we have to define has a radius of What is a circle Radius of a circle Radius what is radius this is a circle its one Radius is What is the radius of a line segment is a line segment is a line segment Because its starting point is the center What is the ending point? One of the points on the circle point is the center and ending point so this A line segment is a line segment meaning If starting and ending point are then radius of circle is a line segment from the center of the circle to any point on the circle What all is included in this on point pay Before Defining Radius We Need to Define circle circle we have to define where This is a circle, we have to define its center. We have to define the end and center of The circle end point is coming somewhere, isn't it? We will have to define these things. We will have to define it, only then will we See if you can write the radius of the circle. What is a circle? Circle is a shape consisting of all points in a plane that r fixed distance from fixed given Point also called the center, what did you say? Bhaiya circle, do you know what a a particular distance from a fixed point Pay go take a point same distance Go get another point at the same distance. Go and take the third point of this circle. The definition is you will study at the same distance Go there and get as many points as you want. Distance pe jao point le lo same distance Pay Jao Point Le Lo Same Distance Pay Point le lo sem distance p jao point le lo sem Go to the distance, take points and all these Join the points and you get a circle. If you join all these points then one If you get a circle then this is what it is said circle is a shape consisting of all points to these Those are points, all these are points, those are one in the plane that are at a fixed distance from a given point so from this given point to this given Fixed distance from point to point If there are points, then what about all these points? has a shape it is non edge it is non edge a Circle is equal to the distance from the center There are also points, if you join them all then one You will get a circle, this is the definition of a circle. Okay, you will study in ninth, so here But he wrote it directly and then after that what is the center center from where from where The distance of the circle is fixed from here. Its distance is the distance of the circle from here. What is fixed, this is the center We already know the point which is such a thing If there is no part then we call it is the radius of the circle so what is defining it what are the points in it that define What are the words that I have to define them, I have defined them too. last part its square square what A square is a kind of quadrilateral is a quadrilateral It is quadrilateral with all sides what happens is equal and all angles What are 90 degrees, so it is a quadrilateral with four equal sides and All four angles are 90 degrees, what all things I will have to define it, now I have written it But people did not understand You told him that he said if you come then you Do I have to tell you first what it is? Things to Do Before Defining Squares to define quadri quadrilateral define I will have to find 90 degrees. So we have to define all these things. What is the close quadrilateral? The figure which has a fourth side Quadrilateral means 90 degrees. If it is a right angle then we have done both these things I have defined it, okay my love, so this was it These are our five definitions, these five, these The question has five parts: one, two, three, four. And these five, so this is question number two. Your children don't understand this exercise. I come because they don't know books I pasted the definition and here comes the book. I have not written it, I have written it myself. If you understand then this PDF will help you You can find it on Tegra, you will understand it. let's go to the next question next A little more brainy question It's a little more mind-boggling This is the question, read it once and start recording. has been What happens many times, my love The recording stops and I speak. I will stay, it is going on, come on, it is going on Look at question number three, this is This is a bit of a brainy question, be careful. Understand Question number three says consider two Some pochle are not necessarily Euclid I don't have any post, I have said only Pochale Ups are just pochales SUP If it happens then you have to tell that such term So let's see given any to distinguish Point is a term there judge any third point The point has come, at least three points There is a point and a line There is a point and a line The first thing we have to define is that the definition of a point and that of a line You will have to tell us the definition, we know it. write Denge R Daaj postlateral concussion meaning what is correct Do they contradict each other? We are not saying that this and this contradict each other. You have to tell me what you are doing and whether it is happening anywhere is also related to Euclid, who If we want to tell whether it is post-lateral to Euclid, then We have done the first part, undefined. term the second part is what is correct and the third Is the part anything like Euclid? Let's read the first one, the first one is given any Two Distinct Points Reading Number One We're reading the first one, Given Any Two Distinct points A and B then there is a point a is a point b is saying there assist a third point see which is in between a and b then a between a and b Point is c is it true that it should be so It could be, it could be because We had read a line which is from point It is made up of many points together It is made up of many points If line A is made then there is a lot in between it All the points are there, there are many points, so one It could also be a c, it could also be a c It may be absolutely correct, the truth is different. There are at least three points that are Not in the Same The line is saying at least means if you No three points should be placed on the same line. If not, there are any points that you I don't want to bring any such line on the same line. I want to make one that is not on the same line as this. If there are points which are not in the same line then There will be at least three points, a, b, and a value. Take c, so we need at least three points. So that a line is not formed, brother, three points One line can be formed from this but if three If there is a point then such a condition can also happen In which there is no line, this is absolutely correct Look, only one line is being made into a single line. If it is being made then it is saying that if Give a task to not draw a single line It was told to you that a single line should not be made. If you want, at least three points for that It is necessary because from two there is always a single line If it is made from two then it will always be a single line. If a third person comes So we can say that yes, now there is no condition. If the third line is not built then we have What have we done, we did the other one We have discussed the second point of things Defined is there any Euclid in it It is working fine, it is working fine Euclid's postlateral line is formed by this It is also Euclid's theorem that two lines intersect at two points. Only one line goes from the point, that's it. Now we have to define its complete I have written the English definition. I will not tell you after reading it because If I tell you, you'll lose your mind If it goes then that is why what I have told you is just that It's okay to write it like this in some way. I have told you what to write for Look at lines, points, and planes. I also initially created the definition plane I told you there is a surface which has a lot of All lines can come in a surface that has a lot An entire surface that has many lines We call it plain, then I wrote this After that, I mean, I wrote the entire definition. I have given this to you, there will be a PDF in it. You will understand completely what I have said. He said that if I have written it here then you will understand. Let's go to the next question My love, the next question tells us If a point c lies between two points a And be sure that's a great bc8 is b there is a point between these two c truth that has given us a ra bc-c Prove that a will be equal to 1/2 a Explain by drawing the figure Figure to be made Given that A is the center of A and C is the center of A. Meaning these two are dividing each other. Are Equally, so we need to prove that a is equal to 1/2 a. We know that A is half of the whole A. Because this is the center, c, so a will be We know that it will be half of the whole. We have to prove it and how will we prove it? Look, I won't do anything Adding both sides Diya and we know and we know we know we know From axiom number two if equals are added Write this one completely if equal are added To equal, write all that down so we have this Add this to this side and add this to this side as well. Both will be equal if the same thing is on both sides The equal sign will remain even when adding There will be no problem a + a is 2ac bc - c It's full, it's 2, it's down to 1/2, it's 1/2 This is what we had to prove, Hans. Proof, that's what we had to prove, Hans. Proof what we did on both sides, add it. If you are adding the same thing then it should be equal The sign of will remain equal to the sign of before. It was equal and will remain equal in future also, the same thing add curry a + a 2ac bc - c then bc2 a This is done, this was easy, the question was easy. There was a question, there is another part of it, that He is talking about the previous question. In that you called C point as mid point Isn't it the previous part in which A B And C is the midpoint. y we get it okay why mid The point is because what A is half B is half We proved that it is of A, with this We proved that a is equal to half a. I gave you proof, I proved that to you now. What is Avery saying to prove? A line segment has only one midpoint We have to prove that there will be only one midpoint. What to prove is just one midpoint. If you want to prove that this will happen, then whenever it happens There will be only one proof Only one line will go, only this will happen How will you do it with construction, he is saying one It will be only one, I said no, there will be two, what will I do? I am saying that let there are to mid point Let let a be another mid point in between Let D be a midpoint Let DD who points it is also a mid point it is also a mid point d also a Suppose the midpoint is then if d is the midpoint which I have assumed then A is also 1/2 of A Equal It will happen brother, we knew it was great from here. 1/2 a when c is the mid point then this condition When d is also the midpoint we will say a = 1/2 A Now we can say these things which are equal to the same thing are equal to one another Axiom number one things which are equal to Same thing are equal one inside another so we will say Half A is also equal to A Half A is also equal to A So A and A also equals a and a also equals a and a also equals so If two things are equal, that is, c and d, then c and d are the same point so they are the same point If two lines c and d are equal then The point is a and a is equal to c and d is also equal to The logical points c and d will also be equal But I had previously assumed that c and d There are different points c also have a mis point d is also a midpoint two different midpoints Now it seems to me that both are equal. So there is a contradiction, there is a contradiction. Earlier I had considered two different mid points Now it appears that it is the same thing that They were different, they are the same, only the names are different. Same Raju Monu both are twin brothers Yes, if there is a contradiction then it means my It was Ajman, she was wrong, I apologized. My ash is there for there is only one How to Find the Midpoint Between a Line Segment You will write in English How do you write like this in English? Suppose is the midpoint of A so means A is equal to A. Suppose another point d is also a mid point So a is equal to 1/2 a so a is also equal to 1/2 a a is also equal to 1/2 a so means a is equal to a will happen because things which are equal to the same Things Are Equal to One Another by Ayam Number One Bye Iam Number One Hens A Bara A Mil Gaya We got A which is A is equal to A it Implies c and d are same point then c and d Same point is it contrasts our ambition there There are no doors, there are four in every line Segment has only one point in the midpoint There will be only one midpoint, see and understand There is nothing, it is easy PG, there is nothing at all. Contradicting, I accepted another mid There is a point but we are seeing both the same Yes, the different points that were considered are the same. If it is the mid point then it means only and only There will be a midpoint between two lines between A line segment is just a function of a line segment. same mid point The next question will be, we just did it behind In the example, the last question is done. Axiom number five says what He says that what does agem number five say agem number What was five? Ejim number five was that hole. Wala that hole is greater than part aegyp What was number five? Aegium number five was hole is greater than part whole is greater than Part of this is what people call universal truth. Why do they say a whole is greater than a Part Universal Truth says so this It has been asked in the question that it is a universal truth Why do they say Why Aegium is listed in Va Ekam Fa Considered as a Universal Truth This is why it is said it is it is it is non As Universal Truth Because It Holds True This will always be true when it is in every field Hold True in Any Field Any Field I will always be true only It will be true everywhere, not just in mathematics. True everywhere, not just in mathematics It would be like I took the example of a globe India is from the entire globe, so it is complete The globe is bigger than that part. A part of pizza, which is pizza So the whole thing is very big, isn't it? From one part of it, it is true everywhere. I am not here just in mathematics We will write it and this will give us our answer. With this, this entire chapter of yours This concludes Thank you so much girl for today. 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