In class ninth one of the biggest chapter I would like to include this chapter pochle five now this is a little interesting I'll go for post lateral, he told us the same thing The point will be such that it brings them above both But what I have read is that from two points only one line can pass There is not much difficult chapter but in this There is a lot of theory in the chapter How are you everyone welcome welcome welcome Everyone to the platform of fix wala My name is Ri, I am yours Mathematics Mander is your friend, your elder brother Guruji, say whatever comes from your heart. How can you do so many things at once? How are you all? Today we are Euclid Geometry i.e. Introduction to Euclid Geometry your class ninth A very simple chapter in my opinion one of the easiest chapter of class ninth I would like to include this chapter in I would like to have your Heros along with this The formula is also quite easy but anyway Rons We will talk about it later, for now today we Talking about Uncle Euclid So brother, he was quite a mathematician pretty big mathematician okay now Understanding geometry means study of shapes Study of shapes where line segments occur yes there is a point, did you understand it there is a line it is quadrilateral It is a parallelogram It is a rectangle So geometry means the rough study of shapes happens okay so skip this chapter Now understand the more difficult chapter than meditation No, but there is enough theory in this chapter it is more i.e. if you often look at maths There is very little theory in it, i.e. on 10 There is theory, you have 90 questions but in this chapter there is no theory on 50, 60 And if you have any other questions then today we will To end this chapter in a short I will take about an hour and give you I will tell you everything, I promise Everyone after this video you will go somewhere else There will be no need to go I will need to ask a question promise this is ok without any delay If we start then friend, well now you see People already mean a lot of things Do you know what a point is and what a line is? what is ray what is line segment what is mid point what is it You know everything roughly, but this chapter When you are reading you should not do all these things. Forget it and read it as if you are new okay in the maths world like When Uncle Euclid was studying all these things So they were discovering that well like this it happens well it happens well it happens okay i will tell you as i can You will understand things without any Let's start with a little delay There will be a bit of theory in the beginning you will see that don't abuse too much Tell me who gives so many theories, let's go So what are you saying The Word Geometry Comes from the greek words geo geometry word The Greek word geo and geometry is geo meaning hota hai arth and metri means To measure is a rough measurement of the meaning As I told you, do the study of shapes Meaning those who do measurement of shapes you can think of something like this okay Geometry Appears to Have Oriented From the Need for Measuring Lands Why would geometry have come to meaning What was the need to measure shapes What was the need to measure Why do you need to study shapes? It was said that geometry was needed Maybe he came because we Lands etc. had to be measured agricultural The land has become commercial land, hey someone It might as well land where you just placed your Friends, you have set foot here, this need Take care of all these little things isn't this branch of mathematics was Studied in Forms in an Ancient Civilisation Look, if I want I can tell you directly. that five to seven AGMs are given five poles and I should finish the chapter but I am I will not do it, I will tell you everything from the basics so that you can understand everything brother where did all these things come from ok good The Greeks Developed Geometry in a Very Systematic Manner When the Greeks Created Geometry If you start reading about it then it will be big I want to start studying from Citymate Manner one by one one by one three greeks mathematicians name thala bhai sahab thales Brother Pythagoras About Brother you know and and and and Euclid brother saheb contributed a lot on geometry Pythagoras' brother, Thales' brother and Brother Euclid had studied a lot of geometry After making the above contribution, let us now see what happens next what happened false proves that a circle is bisected by its diameter now you can say this you already know but still you think like this when Nobody knew all these things when someone I didn't know what a point was what is line what is maths then These people were telling all these things You know the meaning of the first thing, false proof that a circle is bisected by its What did brother prove that the diameter failed What nonsense will you say after hearing this Prove it brother, I would have proved it myself Hey, you fool, he knows a lot of things now that's why bhaiya sahab proved it He said that the circle which is there at that time is his It means that it is bisected by the diameter diameter circle into two equal parts Divides the diameter of a circle into two equal Dividing it into parts will give you this good thing okay I know Pythagoras developed the Theory of Geometry to a Great Extent Pythagoras also contributed a lot to geometry Contributions made by Euclid that uncle euclid introduces the method of Proofing Mathematical Results by Using Deductive Logical Reasoning and the Previously Proven results now which is your problem isn't it the lines end in class ninth Quadrilaterals in Triangles in Angles in circles or in general proof Guruji questions in geometry If this is not possible then discuss about Euclid brother do you prove anything With whose help do you solve some theorems? you are first taught some theorems With the help of those theorems you will get some answers to questions are given and asked to prove it This is a method that is already proven With the help of these things, you can prove some more things. There are some already proven things that will help With this you are proving some more things The way is that with the help of some things, some and proving things this is your uncle Euclid Brother Euclid had brought it, so brother this Brother, he is the root of all trouble, well not anymore But yes, make a huge contribution hey we are joking okay let's go Geometry of plane figures is known as Euclidean geometry geometry of Plane Figures Where you can find Plane Figures Let's read about Line Segment Done Rectangle became Romans became Quadri A figure that is lateral to a plane surface I can make it into a plain figure I say okay so such geometry where Here we study about plane figures I call it Euclidean geometry. His famous book Elements by Euclid Chacha There was a book called Elements He divided it into 13 chapters on elements I had divided it, that means in that book there were 13 There were chapters and there were some very beautiful ones in it The results are based on geometry so this is thick Thick was the history of your chapter where From here came the Euclid brothers and they Contributing to geometry Let's start now and let's talk a little further which was Euclid's book of Elements We can summarize the book in some of these In points, roughly in that book Did he tell all this brother Euclid Surprise work of geometry as definitions euclid Whatever work he has done, sum it up What is a Few of in the Form of Definitions they are given below something is given below now Your chapter starts here right? there is a point is that which has no part bha point if i ask you about point Definition would you say point means this Someone will say point means or someone might say like this Point means something here and something there, point means At that point oh at that point Hey, you say this at that point, right? fat I am trying to say this now just listen You may find this thing a bit strange when you understand it Is a point that is no part of Euclid? Bhai sahab gave the definition of point that What is a point that has no parts? which has no part in your mind now I will have a doubt that what does part mean bhaiya keep listening to the meaning of the part here it's ok to keep on listening a line is a breathless Now I will ask you what is length line If I ask you what is line, you will say line Meaning, something that goes on from here as well which goes on from here also, but What would be the proper definition, maybe you won't give it You may not be able to listen to what I say carefully then he defined the line what is the line what is a breathless Length means line is something which there is no breath there is no breath there's just, only and only line, only and It's just the length, I can understand it, it looks odd It must have been so, but it still feels strange to keep hearing it you will understand later okay ends of Line R Points the Ends of a Line R The points are said to be such that the ends of the line There will be points, there will be points and there will be points I understand you know this too but listen Just find out what he is saying in his book I was telling you all this, a straight line, an Line it up evenly with the points on it What is a self straight line? Straight Line is a Line In which there are a lot of points, very All the points are understood like this they are trying to tell you something okay a surface is that which has length and breath What is only surface like this is a board Like board is the meaning of surface which only And just the length or breadth of the board like this Length is done and this is breadth, I understood it aaya ok the edges of a surface are lines and which is the edge of the surface which is the corner part means this is the surface this is the surface of the surface length and that breadth so the end of this surface is there a part that is a line or not this The end part of the board here is a line is it that you are not understanding On the phone where you are watching this video Its surface is that of your phone This part of the surface is a there's a line there's a line below there's a line here There's a line here, just to tell and explain this trying to be a plane surface is a surface which lines which lines evenly with the straight lines on it self now like she what did you say what is the line bhaiya on which there are so many points what is the surface that Made with lots of lines as if I have done this board took a surface lots lots lots It was made out to be made up of a lot of lines This is what he wanted to say about that time When nobody knew anything, I I know this seems like very basic stuff to you. It has been there but you just keep listening to where it came from Now pay attention to what he is trying to say Let brother Euclid listen to his the definition there is a problem with that if we study this definition carefully if we Read the definition carefully, we will find it that some of the terms like part bha jab When Uncle Euclid gave the definition of a point he used the word part but if he Use of part word in definition of point Doubt will come in your mind about the part what does it mean what does part mean it happens it is ok to listen then bhaiya length breath Even if you give another definition of breath It is also important to explain what the length means It is also important to explain what is meant by If I tell you a line is a breathless one Length then you will say what does breathless mean listen do you know what length means I may not be able to explain the meaning of these things now it's ok to listen by the way here this is very All the definitions were of Euclid, many of them were in it All such words were used which meant Explanation is necessary ok for example in the definition of a point the word Part Needs to Be Defined If You Define part if while giving the definition of point use part part word you have doubt that what is part word i told you I have also explained the meaning of the word part, now part I explained the meaning of the word to you, brother part is something that occupied means something that some area occupied area has to be defined so I will tell you I will tell you something, then you will ask me your doubts I will tell you something and then you will ask doubts Doing this never ends your doubts understand what I am saying we can see that there was a Chain of words, there were many such words which remain undefined there are so many There were many such words Time which will remain undefined and which has no proper Till date no one is able to give a definition of them There is a word point, that is why till today if I I ask you what is the point, you probably You will say point means this point means that that that point till today you are his proper Don't give me a definition if I ask you what is the line you are his till today If you are not able to give a proper definition then something I had to leave some words undefined Define words without leaving them undefined I had to leave some of those words out, they were yours line point etc etc etc etc etc I understood it, it is clear now it is okay to listen So till here you understood some things leaving the words undefined is ok You guys quickly understood the meaning of the words who knows the meaning of point exactly You will not be able to define it, but if you try to define it Chaho a point is an exact location point Means someone is talking about the exact location there there there it is I point okay of the line segment I mean, you know, The Straight Path Between two points a and b suppose I have a point Now you know the meaning of the point Consider a point as an exact location Preeti's house and guess who owns you here Bhaiya my house is Hrithik's house, so whichever one such a line or connecting these two There is a straight path connecting these two The straight path brother path for both of them This could also be the connecting one it could be this as well it could be this as well I can but what can I do about the straight path I will say, I will say line segment, okay what does it mean babu aas to you guys Maybe you know that Ray means aligned segment. Now you know what a line segment means Friends, this is how we denote a line segment If a is a line segment, then it means that I just put a dash above like this, okay, a line Segment when extended indefinitely in one direction is a re a fine as in this Consider the line segment that is your A line A segment is made up of two points if I send him in one direction I will keep on extending it, I will keep on doing it I denote it with an arrow, I call it a ray I will give you how will you denote it, an A ray denote do I understand what I am telling you okay boss good line means a line segment a which I should I extend it in both directions I'll call it line A. How do you denote Suppose if I wrote this over A Arrow If Suppose Above A Such Both Side Arrow What does it mean that yours is something like this Your B and this bus kept moving from both sides it's going on it's going on it's going on so the point The definition of line segment ray and line gives you It's very clear, let's look at it now what does the statement mean very Important statement means a sentence like this Chuch can be judged to be true or false is called a statement i told you something I told you something I told you something Sentence said if you can judge that is it right or wrong is it true or false so I'll call that a statement for I will give you an example now, you will understand it better I will come, why are you teaching me all this? Teach direct action and pallets, all in two minutes The sum of the angles of a triangle is 180 If I told you that Bhaiya the sum of the Angles of a triangle means all three angles The sum of the triangle is 180 degrees now if Brother can you tell after hearing this that this right or wrong yes it is right if you Can you tell me if this is right or wrong means this statement then this is your The statement was made because you were able to tell yes, are you able to judge, are you able to use your mind whether it is right or wrong ok now let's see of all the angles of a quadrilateral is 180 The sum of all angles of a quadrilateral is 180 Can you tell if it is a degree? Can you tell if it is right or wrong? The sum of all the four angles of a quadrilateral is wrong It's 360 degrees if you can tell Whether this is right or wrong then such a sentence I Statement This is also your statement is correct and this is false This statement is a true statement, my point is listen carefully x is 10 greater than 15 p 10 is bigger than 15 this sentence but not a Statement You tell me if I talk to you x p 10 greater than 15 if I told you x p 10 greater than 15 can you tell me You will find whether this is a statement or not. when will you say ment when you are able to tell this It is either right or wrong sir I don't understand I'll tell you if you replace x with 2 If you put u in place of x then this will be your 12 it will come 12 gr 15 friends this is wrong no 12 is smaller than 15 okay but if you put 6 in place of x then 6+10 16 so 16 gr 15 means this is correct So brother, whatever value of x you keep Accordingly, you will understand that this The sentence is true or false if you put x2 So this sentence is wrong if you keep x6 This sentence is correct, but if I tell you You can't tell me if this is right or wrong You will find out because it depends on the value of x It will depend on the value of x If this is right or wrong, you are not sure right now Can you tell whether the sentence x + 10 > 15 is correct? is false or not, therefore this sentence is a statement If you do not understand the meaning of the statement I understood a sentence after reading which You will be able to tell whether it is right or wrong I came now see the best part of the chapter The important thing is that you have a total of seven age groups. and there are five potchle ups if you Only these 12 things read your chapter Exam is over, you will ask exam 2 like this what is it agam thi, i will tell you now I will explain it to you and also ask you to understand the questions first what are aegyp and pochle friends Axium and Polette are the same thing I will explain to you approximately what the difference is. ok is it self evidence true statement I said self evidence evidence means No need to explain this, it is very common The thing that makes sense is self-evidently true statement statement did you understand that such A sentence which you can judge whether it is right or wrong If it contains a true statement, Mathematics In case of then I would call it Axium or Pochle I say okay, true statements are correct Statements that need to be checked If he is right then I will give him a gift or poulet say ok i understood but aegium you who Aegium is a word and you can learn through mathematics do you use aegyptian word completely Meaning of branch in branch of mathematics It doesn't matter whether yours is geometry or algebra You use five words on it, brother only and only geometry only and only Both of them understood geometry, what are they both what is self evidence truth Statements are self-evidently true These are statements meant to prove them I don't need proof of what I told them there is no need to do this this is right this is absolutely right it is a matter of common sense, it is like this statement that is absolutely true I call the statements aegym or pouch I use the word Axium throughout I will use all of them in Mathematics I only do geometry I have understood that there is something like this in my house brother They call me Raj but in this world In this world people call me Hrithik I understood the scene, ok, very good Now look, these are five and seven extremas. Which ones are very easy to understand quickly? Self evidence is fine with true statement are the things which are equal to the same thing are Equal to one and you know these things in maths You are already using it, you know it by now I will tell you once things were not there equal to the same thing things that are the same Equivalent to cheese are things which are equivalent to the same thing They are equal, so they will be equal among themselves too means assume the first one assumes if a is equal to b is and and and and c is equal to b then these two things are equal to the same thing things which are equal to the same thing both brothers a is equal to b both are equal to b if both are equal to b then these two are equal to each other if they are equal then these two are also equal to each other equal ho means this implies means it means both of these mean a You understood it equally, that's why you probably did it in maths You must have seen that believe me brother, believe me brother if it is written a = c or it seems as if it is written if d = c then a b c is equal to d b c equal to things which are equal to the same Things are equal to one another and even to each other It's a simple thing to be equal, boss, think for yourself Look friend, suppose a2 is equal to c also 2 means a and c are equal to Brother, believe me, you are my age is 25 years You are also 25 years old, which means the age of both of us is 25 years. We are both equal to the same thing So we both are equal simple common sense self the next thing is this your use ka aim number one next what if equals are Added to Equals the Holes are Equals Maths Many a times you guys have two equations You add them, right? Why do you do that? yes you can do this what did you say if equals are added to equals then the second means you Let me tell you, suppose I wrote a = b equals I called it equals, for example, I wrote c = d This is called equals so this is an equation this is a The equation is two equations if both of these are If I add a + c then it will come on this side and this side side your b + d will come so if equals r added to equals the holes the holes are also If you understand what I am saying then this I just want to say that they will also be equal to each other if equals are added to equals the You yourself think that holes are equal common sense Suppose 2 is equal to 2 Suppose 4 is equal to 4 then 2 p 4 6 will become 2 p 4 6 that too equal hoga the holes the holes are also equal understanding This thing came to me, this thing became clear good brother what are the third one saying if Equals are subs the reminders are equal What does it mean if reminders are equal Equals are subtracted means if you divide two equations you can add it or subcut it If that too is equal then it means the third assume that a is greater than b assume that c is greater than d if If you minus both of them, what does it mean? would be that a - c okay this reminder b - d this Reminder, this will also be your equal. Implies a - c and b - d are also equal to you It will happen and that's why you guys have two subjects in Mathematics Can we understand how to add or subtract equations this was euclid's third ayem right things which coexist with one another are equal to one another very important things which What does coin side with one other co inside mean? which is one above the other which is one above the other One above the other is equal to one in an understanding things that stick to each other They are equal, for example, I wrote as if I had drawn a line segment okay and it's like I made a rotten line made a segment and it was like I made a rotten line segment made now if you look at the rotten line segment and a line segment one above the other have to inside doing one on top of the other If you are doing it inside it doesn't mean anything This simply means that a line segment is a solid line The segment is equal to a line segment sd is equal to the line segment as if I had point a taken okay and point and point d took which is here now because both the points one is above the other means a is equal to d understand I came across things that are one above the other are equal to each other in geometry, right? the whole is greater than the part very simple sir The whole is greater than the part, I believe I took a chocolate as if I took chocolate chocolate I have written this part of I took this part of the chocolate If you understand then the hole will be from the part It will be huge, just think about it and see the whole thing It must be bigger than a small thing, right brother? This is very common sense and stupid thing but this to which I said self evidence true statement There is no need to prove common sense brother the hole is from that part It must be something big brother, believe me it is complete it is a thing, if I took some part of it then The whole thing is bigger than this part, understand? In aaya things are double of the same thing are equal to one other things are double of the Same thing six and seventh tells you here hoon six things ch are double of the same thing Suppose I wrote A, I wrote it with 2 B's I wrote C equally, I wrote this also as B if you take a break then you can do things which are double of the same those things which are double of the same thing are equal to one another or are equal to each other Things that are doubles of something else are interconnected There will be equal common sense in this you can also put maximum one that things which is equal to the same thing things which are Equal to the same thing both things are same If the thing is equal then both of them are equal to each other I have written the same thing to you in Age Six things which are double of the same thing are Equal to one another and some part of it things which are half of the same thing are Equal to one inside means seven something like this that say I took a that say I took d These two are your half off c This is also your half off is equal to c then these two are also mutually I understood things which are half of the same thing these things which are half of something So for example you can think of the same thing like this Can you tell him that brother the price of Rs. 100 will become Rs. 200 I understood half of it, I understood it, you see This thing has been going on and and and and and and and As if I haven't given it here as an example Don't think that things are okay now that someone else half of a thing are they equal to each other or Your Euclid exam will be done right at your fingertips There should be rote in it and point wise meaning Ask someone about your first exam, this will come to your mind things which are equal to the same thing are equal to one another second axiom if equal are added to equals the holes are equal means you can add the equations to get the third one If Equals Are Subacromial hoti hai fifth wala the whole is greater than the Part Six: Things Which Are Double of the same thing are equal seventh wala aegypti things which are half of the same things are Equal to one, this is with you right away It must be rote now, something like this Important things incident aegis you also People, please read the lines about the lines You guys know what the line is, Bhaiya one Line segments are infinitely long Produce that one line in direction If it is formed then some thing about the line is aegyp Read Aegium means self evidence truth Your statement is very true Important Align Contains Infit Many Points It's a simple thing, there are many lines Infighting is made up of points Point How many lines can I draw with Ifatop How many lines can I draw from a single point I can make a lot of any one point I draw lines with lots of friends can I understand what you are saying look Nana How many things can I expect from this one line and one point lines infinitesimal I understood very well what is written next Important: Is this important to you? what should you write brother one and only one one and only one line can be drawn to pass through to given points a and b now this is very Is it important that there is only one Only this line can pass two points I mean I made a point Exact location as if it was a point I have b from these two points friends only And how can you believe that only one line will pass You took a line from here as if from A You can take a line from A to I will touch this B, there is no problem I understood that I should extend it further I give you I understood bro why like this now yes forward Up did you understand it, look there is only one line which is a Can anyone pass both B and C? There will not be a line which passes through both A and B. Don't do this, there will be many such lines There will be many lines that pass from A to B A point has many lines that pass through A This line is passing through a but this line is passing through b I cannot pass common sense, believe me this line is a she is passing from b but she is not passing from c common sense will think this line will pass through A It is happening but she is not able to pass with B in common anyway friends there are lots of sense from b also the lines will pass but only from b and a and I understood that only one line will pass Only one line passes from B to A by doing two points only and only one the line passes a unique line passes it's very important okay now five There's a lot of talk about polecats Simply put, the first one is the same, bhaiya a a straight line may be drawn from any one point to any other point what are you saying a lot Look at this stupid thing, you people take these things easily It looks like that because it was then At a time when no one had read anything These are pretty tough things according to how You will understand what a straight line is, right? what is the point etc what is dim kana what is it okay what are you saying A straight line can be made from one point to point it is so simple i just did it took one point or took another point in Together I made a straight line I could understand it and that is what you need right now I explained to you what is pochle one boss so now I explained to you Euclid Awesome that there is a unique line joining two distinct Points Distinct Meaning Different Distinct means different and co-ed Meaning same distant point means different Point coside means the same point is above the other One is distinct meaning different points Inside means coincidence point means one what is the point above saying Euclid brother, brother what you just read Did you read the last thing yet? that from two points p and q only and only A single line can pass a unique line Yes A lot of lines pass by and a lot of all the lines will pass many more than q The lines will pass but those lines from p and q There is only one line from both points Why did you say that you will pass with different points? Because suppose if p is this and q is above it So this is just one point and one Many lines from the point can pass you by That is why he said different points So this is your bottom one from just two points And she will pass just one line to him unique line bola punch to very easy a Terminated line can be produced Infinitely mean terminated line Mean line Terminated line referring to segment Meaning the line stopped talking about line segments If the line has stopped then consider it as your A line is the segment as if your A is a line segment You can extend it in both directions How many stupid things can you remember? but okay what was number three A circle can be drawn with any center any Look at the radius and how far you are already know circle you any center You can draw a circle using any radius You can take any center, any radius You can take any center and any radius You can do Dr. from any center can you draw with radius did you understand did you understand this circle can be given to you be done with any center any Rey look ahead what was the fourth plate, right What does it mean to say angles are equal to one another Brother, if a right angle is being formed with Pluto Well Pluto is no more, okay Saturn If a right angle is formed in the planet with A, in this sense a right angle is being formed. Or a right angle is being formed with Jupiter Everywhere right angles are formed, everything is perfect are equal and it's obvious why because right angle means 90° how stupid The point is all right angles are equal to one And so for example friends, suppose I As if I agreed friends this is the right angle As such I made this, I said ae to this, I said oh to this said B and suppose I made a right angle like this made it, said it C said it B said it d then AOC will be equal to all right angles It's a simple thing that we are equal to each other, it's okay pochle five now this is a little interesting it is a problem please pay attention as I said friends theory is theory understand it a little Very interesting, very easy, what are you saying if a straight line falls Let's take a straight line, I will direct you to this Meaning friends, you understood these two straight lines These are your two straight lines sir, consider them as one pass them both in a straight line As if passing by these two in a straight line I am getting it done, you people might know about it I call it transversal but I don't know anyway It doesn't matter if these two lines are straight I'm fine if I pass a straight line from Both are straight lines, which side are these Play Fairs is telling you this Aegium I also call it Pochle Five Can you see these two lines now? You will find her on this side, these two brothers, if you If you extend both of them infit then this will go ahead She will go away, both of them will go ahead someday you will not meet on this side from this side both Will meet you very soon somewhere here If you understand what is going on, you will get it This play is fairs ageum or fifth pot Let me tell you where the two lines meet But it is found on that side where The sum of these two interior angles is less than 180 yes, if you pay attention, will you understand This angle plus this angle together It will be more than 180 and that is why on that side I can't find the line where both are The interior size is more than 180 Where will you find both the interiors will the sum be less than 180, do you understand the same thing It is written if a straight line is falling on two straight lines makes the eightieth angle on the same side of it taken together less than Two right angles less than two right angles means less than 90 brother two right angles What does it mean 2 * 90 means 180 degrees If you understand it then brother, interior angle Where the sum is less than 180, it will be you will get two lines, easy, ok Now what happened after this letter on fifth pollet was muddied as under later on a little bit After some time the fifth paw was slightly modified What kind of things were done, what kind of things were said, brother, brother for Every line L and for every point P not lying on l any line will be l and any Your point will be to listen to me carefully. The line will be L and any point P will be I I make it separately as if any line of yours a and any point p lying on the line L not doing that which is not up to l which is up to l which is not above l this what are you saying that from the p point only and only one line will pass like this good now You guys know that there are many things from p point Lines can pass from one point to another point I can pass many lines, but only one like this There will be a line, but there will only be one such line which will be I understood that it would be parallel to one such There will be a line which is parallel to L, say I understood it and wrote the same thing what that bhaiya for every line a and for every point p not lying on l their existence A unique line m passing through p and parallel to l did you understand l there is a line p There is a point not on l which is farther than p All lines will pass but only one such line There will be a unique line parallel to l it will be there which will pass through p, it is simple to understand Gaya bus to distinct intersect lines can not be parallel to the same line what does it mean Are you able to understand brother, good distant means different then two different intersect ng lines means i took a line like this Suppose if I took a line like this then give it to me listen to intersecting lines two intersecting lines lines cannot be parallel to the same Both lines are not parallel to any same line It may be a simple thing, why don't you look at it If I draw a line parallel to this line, say here If I draw a line then it is parallel to this, but Is there no parallel to this, why is it Intersector brother there are either intersecting lines or Parallel lines are either one above the other There are lines brother, there are only three cases right The lines will either be parallel or will intersect at a point or each We will intersect at a point which means above one Now what are these people saying if they are united there are two different intersecting lines, that means If it is intersecting at a point then it Both lines are not parallel to the same line for example suppose I said one line made here which is parallel to this but it is different from this it won't be parallel because if you take it forward If you increase G then both the meetings will be set up Parallel lines also mean that They should not understand that there should be no meeting It went great so these are your five Paulettes It's done, let's recall Politan once Bhaiya that from two points there was only one The line will pass, what was it brother A terminated line is referred to as a stopped line. You can extend the segment from both sides what was the third one can you make a circle You can draw a line from any point and to any radius lekar putt four are all right angles to each other Poletas are equal to There are lines, I made a straight line like this okay what will happen is these two straight lines The sides will meet where the sum of the interior angles It will be less than 180, very good, let's go brother You have understood all these things now. What is the meaning of theorem? Have you read Aegis? you understood it seven times, you understood it earlier Five Now in Maths you will get a lot of There will be theorems, listen to me carefully Axium and Pochle require you to proofread I don't need it, I'll give you everything After explaining and explaining with proof You don't need to prove it She is self evidence, meaning she has common sense I understood the point, all the right angles are with each other are equal to two intersecting If there are lines then parallel to these two are only and Just means there is something common between these two parallel There will be no line, all this is your self evidence There are things but you have to prove the theorem Axium and Pochle Dozen need a proof but theorem needs a proof you can prove it We have to prove that this is also a true state A theorem is a true statement Yes friends, this is also your true statement happens axiom is also true statement The statement is also a true theorem is a true statement but you need to know the theorem You have to prove Axium and Pot Now you understand that you are driven by true value I will teach you the meaning of the theorem statement that requires a proof is called a theorem simple stub truth of theorem i Non Proof If someone asks you for a theorem proof Show it by doing it, it means you can prove it You are saying that he wrote the correct statement, okay For example if someone says this to you bhaiya sam of angles around point 360 means any All the angles around the point will be equal to 360 for example I made this angle, this angle, this angle, this The sum of all the angles will be 360°. Proofreading you You will have to understand the meaning of the triangle You also have to prove that it is 180 I will prove it to you right now Triangle Wale Chatter Achcha Kolari Meaning Don't you guys think it doesn't mean anything right now You people should not understand the meaning of Kolari right now any meaning ok let's go to this chapter now Friends, you have to prove a theorem. It will be said and this is the most important part of this chapter. This is an important question please be careful Watch and after this I will give you some MCQs I will ask you questions and then your chapter will end ok now just for the questions It's his turn, I'm giving him a theorem You will have to prove what the theorem is Prove that two distinct lines means two Talking about two distinct lines you are doing this meaning of two different lines because Friends, the line can also be the same as if a line I took this and one more on top of this so this There was a coincidence line, he said two different lines can not have more than no one Point in common of two different lines I do not consider any point more common than this I took one line, I took one line, then these two there will be only one point common in Not more than one point should be common only and Only one point will be common to more than one You need this proof that the point cannot be common It's a pretty common sense thing to do If you pay attention, if it is produced further do this further produce same point There will be one who is worthy of both There must be a point, apart from this there must be some other point can't see both of them apart is diverging from and Here it was already diverging, so You have to prove that there are two different Lines do not have more than one point in common That means there will be a same point on both those lines It will be like the same thing coming on both lines The point should be such that it lies on both the lines How to prove that you won't have many points See how to proofread Pay attention to proofreading Write it down completely because it is very important It is easy too, what are you saying brother saying look if l is parallel to m now there can be two cases what if two different lines are understood if two if two different lines are two different lines There can be cases or your lines there will be intersecting meaning either in the lines There will be some like this, you will meet them somewhere or else It is possible that your lines will be parallel I will tell you again, there are only three cases, either The lines are one above the other due to coincidence or then the lines are parallel either the line It is intersecting, go ahead and see Now it will intersect, now this is the case no because he said two different things If there are lines then it means two different lines It is not possible that both of these will happen, so what will you say? if i is parallel to m then clear there is no point common to both l and m then One thing is clear, brother, if two lines are parallel then any point between them It will not be common, I understand, okay brother So this thing is clear, now we are going to talk about that case Let us see when l is not parallel to a then there are two In this case either l a is parallel to l a or l a is parallel to l a is not parallel to then in this case even one There is no point common in both of them in this case Let's see how many points are common and how to prove it If possible I will accept it He told us that there will be only one point which will I assume that one will bring it upon the I assume that p and p are points greater than If q is two points then l and a both have a are mean mean mean mean mean p and q P is coming in this and q is coming in this too and p and q are also coming in it such value I assume that I am going along like this, okay, but if I will assume that this is the problem what is then l contain both p and q means l p and q are also coming in the line and m is in the line I am also getting your p and q, keep listening be careful but we know one thing but we know that there is only one line passing through to Distinct points p and q bhai i man Let me leave it, brother, P and Q should also be included in this. and p and q are also coming in it like this I take it for granted, but what have I learned that there is only one line from two points pass the tax can only one from two points can pass the line and if you pay attention What happened to these two because of my belief This line is also passing through the point and in This line is also passing through both the points What did you understand brother, what do I have to prove? That is, brother, in these two lines, there are only and There will only be one point common and that will be somewhere here it would be I'm assuming that a more than one point will be common have more points in common means that whichever two There are points, they are coming in this as well and They are coming in this also but it is not possible why because from two points only and only Only one line comes out, but I believe Because of this, l is also coming out and m is also coming out so that's it but we know that there is one and only one line passing through two I understood the different points and they became clear This Contrasts the Hypothesis That L and A Are Distinct This Contrasts The Hypothesis That A&AR Distinct Just mean it Distinct lines cannot have more than one con point in common simple what did you understand what is happening am I understanding what tell me brother we accepted that p and q come in this too and we assume that p and q also come in it. But it is not possible, right Bhaiya what will you write that let's suppose let's suppose there are two points common to a and m This means p and q lies a p and k lies on A but now you say but this is not possible why Because there is only one and only one from two points She can pass the line, but I have no intention of believing this Because two different lines pass from two points she is doing this, this is not possible so we are last what will I write this is not possible hens Our Ajman Vaj color was ours Ajman color was ours It was wrong to believe that these two points Common there for there is only one Do you understand what I am saying I understood what you want to say Surely, boss is there, let's go ahead and see now some questions are very easy what to say if a point sea lies between two Points A and B are really that big bc8 c lies between two points a and b ok so there are two points say a and b Point C is lying somewhere in between Now it is in the middle, not necessarily exactly in the middle I am in the middle, as if I am lying here what have you given to me what have you given to me The way to bring your a bcc950 I have been given a great bc2 of a is very easy proof by the way ok let's see so a is needed here a what did i think of put a instead of b to bring b to replace a to bring a plus b to get a instead of b To get to A position you will have to do A+ What did I think that both sides You gave me a plus, tell me one thing a is equal to a, isn't it? a is equal to a This is a very simple thing isn't it ok now look at one thing brother why is a equal to a things which can be found inside within a and a There is only one thing I can understand now I called it the first equation, I called it the second Euclid's equation According to Euclid's second aegis, if Equals are added to equals if I add the equals If I add equals, then it will be will also be equals or you get 2ac b p a coside with b s p a brother b c p a Are you understanding what he is doing brother BC and A coming over A means coside is doing means it will be equal means equal I think it must be Euclid's formula things that happen with one another are equal to one another to 2ac your friends equals a There went A, your half A is equal to look. It is very easy to prove it but it is very easy to use it I will tell you how you are proving it by doing it. I am trying to teach you, I understood it Very good brother, please go ahead what are you saying its easy and giving me beedi I am giving you A equal BD, okay so You have been given equal BD, what is the proof You have to give something and what else you have to prove Do you have to prove something equal to you is there some equal amount of this, you are given this Instead you have to bring a beedi given to you did it happen do you want to bring sadi instead I am understanding the point, understanding the point again I'll say you've been given A instead If you want to bring it then tell me what should I do A come I will tell you again see you have given A it has happened that instead of A you want A then from A if If I remove this part, it will come out meaning I have to do a minus, what have I thought of you are the same as before this beedi is of beedi If you want CD instead then in BD if you want this remove the part that says CD and you will understand When I came, just think about what you were thinking In Proof Look, okay, you know that Bhaiya a Barab It's a simple and buddy thing bcc950 I removed this thing I removed this thing aa save Here you have written that A is equal to BD If you remove this BC from BD then the rotten thing will be saved The answer has come friends The answer came exactly the same, aunty cd easy sure ok boss let's go very easy what are you saying angle one equals 3 angle two equals 4 given to you angle one equals angle 3 given angle to you equals angle 4 given angle to you He told me to make angle A equal to C, he told me to make angle A means this is a completely equal angle C how to do it how is it being made 1 p 2 how is it becoming possible by doing 3 p 4 so i have done it have you used a lot of brain, this is his first said this the second one said aim number two to if Equals are added to equals if equals are added to equals the holes are equal angle 1 p 2 angle 1 p 2 friends angle a is angle 3 plus angle four your angle c is ho I understood how you are doing it very easy ok ok ok ok this one Let the second one be very easy you will do the first one as homework, i will tell you I am doing it for you or I will tell you in the comment box answer it Friends, you can give the answer in the comment box it is okay to write and tell that together How did you feel? We will learn from your comments. yes friends we will prove it if we do something People have made mistakes, what can I say? stay good brother bc-c is given to you, exactly the first one A equals Prove bc-c is equal to a mccc.in How will it come is given in the question L and A L and A are the midpoints of A and BC What is L, the mid point of A, do you know is this equal to this and a what is the mid of bc Points mean this is equal, you know these things Everyone understands the meaning of mid point, right Boss? that if this is the midpoint of A, that means equal to this if it is the mid point of the busi means I am able to understand this clearly, let's see how I will do it, see I have given it to you Do you know one thing that A is equal to B pay attention ok a p a b together become a you wrote this a p a You wrote b and bc and a p a b s You wrote b a p ac, now you understand this I want this and I want this, I left it written LB's Jag instead of lb you can write lb mid point is written in place of bomb b ki jag b ki Place ac mid point a p a answer aya aa p a a If the AC power supply is disconnected from the AC then the I got your answer, I understood it How did I understand the proof? how are you looking karam I told you apk why did you write because a pay attention aps ab inside is A with A p A b over A then A has to be you wrote a p a b yam number four things We coside with one another are equal to one and then why are a, b and a equal wrote because l b and a are equal because This is the midpoint because BA and MC are equal This is the mid point so you can write BM as MC can you write a album do you understand The second one is for you to do your homework Answer quickly what is Aegium R Aegium Exims R Aegium Definitions Hoti There are no Aegium Theorems Aegypt R Universal Truth means true words As I mentioned, Aegium and Pos true words true words means the self is right evidence true statement sense to own This word also speaks of universal truth I probably forgot to use it, okay? Axioms are also universal truths Polecats are also universal truth you This truth is true no matter where you go Universal Truth Specific to Geometry Universal Truth in All Branches of Math Option number D is correct both esim and pollet There are universal truths, but aegyptiaca you use through-out mathematics and You can only know about polets through geometry I use next what are you saying which of the Following is the false statement among these Which is the fall infighting? passing multiple lines through a given point it is true a unique line can be drawn to pass through to receive to given Points are only one out of two points the line will pass the unique line is correct this too Re A is equal to Re B is this correct for Re A Meaning Ray A means friends Ray A means brother or something like that and Re Bi means and Re B means As such Some Re Bi means this, I understood the matter BA means that it is extended from A and that too is A Meaning if extended from B then these two These are two different things, friends y your wrong state is ok hey only one end point exactly There is only one end point of this ray Ray has only one end There is a point and it moves from one side A caste line has only one end point It happens that she goes on walking from one side Your answer became correct only because you wrote it wrong come on brother what are you saying what are you saying what are you saying bhaiya bhaiya and what is the public saying, all this is easy for me think it's ok let's go to Euclides witch Axiom Illustrates the Statement That When x p = 15 x p p h = 15 p set brother if if x p y = 15 is written So I will take this as an po ps root equals 15 ps then I can write hmm i basically did what i basically did what did you do brother it was written 15 I added a root to the left hand side as well I added J on the right hand side as well You know, both of you are in an equation Side Any Same Cheese D Subcut Multiply You can divide, just multiply and divide I am not doing it from zero, so brother I will do this I can do it but what kind of thing can I do? I am not able to understand which SIM Guruji is this friends j equal j you know if equals are added to equals the holes are equal x pwa pj 15 pj this is also equal amount number M You understood the number, you can do this with the help of second m can we say simple a is of the same as b a that j is equal to b is of the same age The edge b of the edge c is also equal to b Euclides Which Aegium Illustrates the Relative Ages of a & c Which aegis of Euclid do you will give the edges of a and c if things which are equal to the same thing Hi both these things are same thing These two things are equivalent to the same thing things which are equal to the same thing are Equal to one within means the edge of a and c Ageium number one things will be equal to you too which are equal to the same thing are equal to Forest inside ok boss ok sir euclid stated all right angles are equal to each other in the form of a pochle easy poplet number i think three It was three, it was three or four, something like that let the lines are parallel if they do not intersect is stated in the form dosto lines are parallel lines parallel if they are not intersecting or Who told the definition of polet to Ayam ne do your polet told me to remember play I did this in fair time okay let's just go to euclid's second axiom what happened bhaiya if equals are added to equal The holes are equal, this is how you should remember them I just want to show you some questions Euclid what was the fith polet bhaiya good second It was Aegium, okay, what was Fifth Polet, brother? if a straight line is falling on too straight line makes the interior angle Same, I taught you two straight lines is a straight line passed The sum of the interior angles on which side is less than 180 There will be a meeting between those two lines What will be your next step? Double of the Same Things Are Equal is okay something that is double of something else Things that are double of something else and are intertwined with each other will be equal, I understood, okay, what else Bhaiya I am R so I have done this ok tell me this is the last two question of the the day if a straight line falling on to Straight lines make the interior angles on the same side of it who some i 120 what say brother keep straight lines it's as if you have two straight lines there are two straight lines and one more straight This is the line which is passing these two what did you write if a straight line falling on two Straight Lines If a Straight Line is Falling on two straight lines makes the interior angles on the same side of it who's some is 120 So friends, believe that these are becoming your interiors. or your interior is being created as if imagine Do this so that the sum of these two is 120 degrees. is it equal asked ok then the two straight lines which are two straight lines are produced indefinitely meaning if They should be produced meet on the side on wich the sum of the angles is meet on the side on which the sum of the angles is imagine first So let me tell you this thing like this So you will understand from the diagram, okay? Look, imagine there will be a diagram like this imagine okay and this is your straight Now let's say the line is this interior and this interior What is the difference between these two interiors? 120 so which side do these two lines meet I will do this to you, you just know friends Both lines should meet on this side of you. Did you go? I taught you both. The lines meet on the side where the angle is The sum of is less than 180 is less than 180 is less than 180 If it is less then this is less than 120 or 180 and you understand that Equal to 18, I understood it, it became clear just for sure What are you saying next? Excellent question. Prove that every line segment is only one mid point proves that every thing is very good This is a question that you might be asked about Euclid Pay attention to what you say in geometry I am proving that every line segment has meaning Every line segment has the same midpoint proves that every line segment has had the same mid point i.e. I would have drawn a line Segment taken A Mid point means a point such that a point which divides A into two equal parts in the question to prove that any Two line segments will have the same midpoint No midpoint or not more than two How to prove that there is not more than one I agreed that bhaiya c its mid point I considered C now listen if C is the mid point If c is the mid point then i is If let c be the mid point Suppose I took C to the mid point focus give if s is the mid point then a is equal to bcc950 is inside the A to A it has come so It is a very simple useless thing [music] bc9 four so your a is 1/2 of a your a Here comes 1/2 of A. Did you understand this? If I let c be the midpoint now I I agree that ok brother d is also the mid point I agree that ok brother d is also the mid point Let's see what will happen if we consider the mid point as if it is here and I believed d is also mid There is a point, but we know it's common sense that there will be only one mid point, how can there be two points which can divide the line into two equal There will be only one mid point but I madi is also the mid point then if d is the mid point so your a is equal to d b your a is equal to d b This is now understood by both sides Friends, I added A A to A P a equals d b p d b sorry What is the benefit? See what the benefit is, pay attention So A P A becomes your 2 A and B P A todi b p edi b p a bhai jaan b p a y is cosiding with a y your equal to a Now what will happen from here that whoever is A Your half A is equal to A and your half A is equal to I understood it well, now let's talk about the first one look and look at the second one some Euclid I am missing Axium what a Eddie both They are different things but both are equal to the same thing these things are half of the same things ch are half of the same thing these two ac and Eddie these two are A and Eddie is half of A meaning If both are equal then by one you get Ba by ayam you guys can write that a and AD are equal and when A and AD are equal can you use your brain brother from the diagram And AD does not appear to be equal to A from the diagram And Eddie is not looking good, it means something is wrong It is because of the diagram that A and AD are not equal You can see it brother, when I solved C and D Taking different mid points then A and AD are equal A and AD came equal, only one such came This can happen only in the case when C and D are the same point when c and d are not distinct points they are one it's the same point it's the same point it's the same is a point means any line segment the one and only one of Did you understand what I said? what did i say here or you are like this understand what I am saying, did you believe that one The reason for your belief is that the midpoint is greater than If something wrong comes out then you write this is color there four our ajman was rang hens there is only one mid point off ay I will say it again did you assume that from one There is more mid point for you to believe something Because something wrong happened brother, it is wrong right Common sense is wrong, brother, equal to AC AD I can't see it, it's common sense, I will understand it Something is wrong because of what you believed if it comes then what will you write this is rang this is not possible and why did you come like this you must have done something wrong for sure It was wrong to believe that I must have done something wrong that there is more than one midpoint of A and You will have only one mid point like this The second thing is to write in English it is much easier and what can you do if I assume that if A equals Eddie comes then It will only come in one case when the CD is is this the only possible thing to be above the other write you yes I this is only possible I this is only possible C & D coin side when C and D are one above the other A understood it and if C and D are of one above is a delayer delayer four c equals d sss sss there is only one mid point there is only there is only one mid point of line segment A off a okay the direction of the line segment that made the sign ok This is how it ends on Datchi, almost no i have got you covered Now after this just go and do your NCERT. Simple, remember these three things: Aegym Pochle You have to prove every theorem There are five axioms and five universal truths They don't need us to prove it there are seven aegyptiums, five pochle, and in the middle I told you some more small things Do the questions and your chapter is over Hope you enjoyed it, you understood it now I will meet you guys in the next chapter me that is lines and angles one shot her it will be available soon, forgive me Please do it, there was some issue with the mic This lecture got delayed a bit sorry seriously i will meet you Till then in the next class from the people take care and let me know how you feel Bhaiya lecture, are you facing any problem So please share it with me and who else Please tell me which chapter you want from it What is the problem? Tell me everything in the comment box. hai love you all ta bye bye and take care bye Bye