This video teaches fundamental geometry concepts including: (1) The sum of all three interior angles in any closed triangle equals 180 degrees; (2) Types of triangles - equilateral (all three sides equal, all angles 60°) and isosceles (two sides equal, base angles equal); (3) The exterior angle theorem - the exterior angle equals the sum of the two opposite interior angles; (4) A straight line measures 180 degrees; (5) Vertically opposite angles are equal to each other. These foundational theorems are essential for solving geometry problems and understanding more complex geometric relationships.
Deep Dive
Prerequisite Knowledge
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Where to go next
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Deep Dive
MY ONLINE TEACHER is liveAdded:
Okay.
Wow.
waiting for my student before we start the class.
I'm wait for you before we start the class.
Okay.
Okay.
All right, I'm waiting for you guys. So, please, as we waiting for others, let's encourage them to be there. It's only one person that is live now. I would like you to just say hi.
If you can hear me clearly on the comment section, just say hi.
All right. Okay. We have two people now.
I want us to get like five then we'll start. Just five then we start. I've prepared my notes. Everything is intact today. And and I hope you can hear me clearly. All right. I just want us to reach five then we will start the class.
Wow, we have five people ready please.
Um, good evening guys. Um, let me just say happy preparation for your WK. Wow.
Wow. I can see the love. That's a good one. Happy preparation for your WK. Um, but what I would say is that put your mind at rest. All right. You are in the right place. You are in the perfect place for you when it come to the matter of preparation. When it come to the matter of preparation towards your W. So simple as ABC. So in my class, I'm going to be making it as simple as possible.
All my classes are going to be as simple as possible. In fact, sometimes I'll begin to use some method that you use when you are in basic classes, GSS classes and you will see the way you will really love the class. All right.
Okay. So let me start with this. So tonight I'm going to be dealing with geometry and I will start with a very simple topic. I will start with triangle.
So now I like you can see me clearly if you can see me clearly just type in the comment section just up in the comment section. All right I want you to know that every triangle has a sum of 180 a closed triangle. Please pay attention to that. You know, triangle is the shape that has three sides. Now, okay. Wow.
Say hi. That's a good one. I love that.
Now, if I have a closed triangle like this, A, B, and C, sorry. And C. A + B + C is equal to 180°. That means let's start with our foundational knowledge. All right. Let's start with the foundational knowledge that the addition of these three sides equal to what?
180. Many of us know this before but I have to just remind us about it.
Addition of A B C is what 180. Now after knowing this because in some of your questions they will not just ask you this but is part of the thing that you need to know when it come to your preparation. Now let me take my notes.
That is the first theorem of geometry that you must know. Now another thing I want to take you to is what we call the types of triangle. Many people I've seen many students uh not paying attention to this not paying attention to parts of triangle and they've missed a lot of opportunity or a lot of answers. But before I continue let me just say this if you have not subscribed to this YouTube channel you are not doing us good and you're not doing yourself good for your preparation and we encourage you to subscribe to this YouTube channel. If you have not done that just go and subscribe like what usually see doesn't bite. Just go and subscribe. It really help us and encourage us. Now let me continue with types of triangle. All right. Types of triangle. Now you may like we are here for something serious.
This man is teaching us about triangle.
Yes, you really need it because by the time I begin to take one law, second law, third law together. You will see that you really need to know this type of triangle. Now the first one is what we call equilateral triangle. Now equilateral triangle has one features all sides are equal. Wow, we having turn out already 29 people on the live class and that's a good one.
Equilateral equilateral triangle.
And when it come to equilateral triangle, all sides are what? All sides are equal. Look at it now. This side, this side and this side, they are equal.
That means the length of this plates is the same thing with this one. is the same thing with this one. I want to get on that. Now the angle too will be the same thing and that will be 60 60 for the sake of those that doesn't know before but in most of the drawing I don't usually see equilateral triangle.
I usually see isocles triangle and I will be explaining how to know if the triangle is an isocles triangle because I've seen some questions and some questions and like and I see some of my students they were struggling. I was like this thing is very simple. Can't you just see the isocles triangle? Let me show you how to get triangle.
Isocles triangle says only two side of my equal. Now second I hope all of us have written this equilateral triangle.
If you have not done that please quickly do that now because we have a lot of things to cover. That's why I'm rushing.
All right. We have a lot of things to cover. That's why I'm rushing. All right. So I don't want us to spend too much more time on this foundational knowledge because now the first one is what equilateral triangle and in equilateral triangle all the sides are what are equal and all the angles are also what equal. So add that foundational knowledge. Then the second one is what we call isocence triangle.
Isocalence triangle.
Now pay attention to this. This is very very you need to know it because I will bring out some questions and you see that you really need to know it. Now isocus says that only two sides of mine are equal this side and this side the base is not the same thing as the other side. So if this one is 2 cm and this one is 2 cm this one maybe 5 cm there about that mean this side is different from this and this one is equal to this.
Do you understand that everybody? I'll do it again so that you can get it.
That's why we're in class. Now I will explain it again. Isocles triangle is a shape that only two sides are equal. Now where this angle is facing and where this one is facing will be the same thing. Why this one will be different?
That means if this one is 30 when we tell our x our two will be 30 because this side is 30. This place will what?
30. Do we understand that now? So if our S is 30, who can tell you what our Y will be? Our Y will 180 - 30 + 30. Why? A closed triangle is what is 180. Do we understand that everybody? So you need to know that and have that at the back of the mind. You see have other types of triangle triangle, we have right angle triangle.
I'm not here yet to explain that because by now I think you should you should know that by now I think you should know that by now I just have to explain this because I'm going to be using more of this is triangle in some of the question that I saw all right now let's move on to the second law the second theorem when it come to geometry the first theorem says that all the s of the angle in a triangle are what they are 180 so let me give you just 30 seconds or 1 minute to copy all the notes that is here. So please you can copy it then I'll come back just 30 seconds copy the thing that you are seen on the board. I explained a closed triangle that the sum of the angle of the triangle is what 180 the sum of the angle of triangle is what 180°.
So write that now please write it. I'm just giving you 20 seconds. You have to work as fast as possible. So after 20 seconds then I'm going to clean it up.
Then we go to the second theorem. The first theorem is that all the angle a triangle is 180. All the three angles are what they are. Wow. A question. All right. No question. Please if you have question or you have concern go to the comment section just type your question or type your concern. I'm going to I'm ready to answer you straight forward. So we are here tonight. No shaking by the grace of God. All right. So that's the first law. That's the first theorem. All right. So please quickly write it. Give it just 20 seconds to write what is on the board. Then we'll move on to the second theorem.
All right. By now I think all of us have it by now. I think all of us have beating it. So let me clean it then we move. All right. Okay. I'm seeing hi.
Some people saying hi. Please move on to the second theorem. Straight forward. There's no time to check time though many of you people are not joining the live class yet um I'm not it against you I hope everybody believe that you not always have free now let's move on to the second one wow let's second theorem let's move on to the second theorem of geometry the second theoreance is let me let me again now So tutorial two interior and inside the triangle from the interior and inside the triangle from the what? Interior inside from interior inside. Why the extent? All right. Now, like I was saying.
All right. Now, like I was saying.
Okay. I think we having some students are having issue.
All right. So, even if it is just one person I have, I'm going on. So, it's is in the hand of us to join and like, right? Don't forget what I said that you should subscribe to this channel. If you have not done that, please go and subscribe. It will really really help us to uh promote this platform. So, let's go with our class. Now, like I was saying that we have the interior angle of the triangle. The interior means inside. The exterior means outside. Do we understand that? So, the interior angle of the triangle at this angle 1 2 3. This is the exterior. Are you with me? This is what interior angle. Then this is the exterior. Now angle is the same. So yeah. So sorry guys for that uh little. Now let us continue our class.
As I was saying that okay it is like you switch left to right. Okay.
Now, do you like is it okay now?
Is it okay now? Thank you so much for that question. All right. Thank you so much for that question. I love that. It depends on the camera the way you are around your camera. Now, let's go guys.
Like I was saying that we have interior side of the triangle which are the angle inside and we have the exterior side.
Now the sum of this interior angle, the two interior angle is the opposite of the exterior angle. Another example, imagine I have something like this and they gave me this one to be 30. They gave me this one to be 40° rather. Now I say this one is x. That means I'm going to be having x my x 30 + 40 and that is 70°. Do we understand that the addition of these two sides is the addition of the two of them is this exterior angle. Do we understand that? That is the second theorem that all of you must know. You must add them at the back of your mind.
The first one was that a close angle is 180°. The second one is that the sum of the two interior angle is the number of the opposite exterior angle. Get it right? Look at this example. If you don't understand my explanation, look at my example. Look at this example.
Addition of these two sides equal to what? The external angle that is X. Look at this one. Now imagine I have something like this. A triangle like this and it's extended like this.
A triangle and it's extended. And he said this one is 40. And he said this one is 50. And he said I should look for X. Very simple. What am I going to do?
What? X is equal to what? 40 + what? 50 and that's what 90°.
So please quickly copy this within 20 seconds.
Please quickly copy this within 20 seconds. Then I will now move on to what we call angle between lines. Then I'll now begin to take some wire questions.
You will like this class. You will really like it. If you are having any complaint, just do well to just type it in the comment section. Sir, this is my complaint. Then we are good to go. So 30 seconds to copy this then move on to the next layer. Thank you. 20 seconds. Then I'm moving on to what I call angle between lines. This we did it. You have done it in your GSS2. Yes, I believe because this is my field is the DSS2 topic. So I'm going to teach you again because you truly need it for this. So please quickly copy this within 20 seconds then we I will clean it up.
Then we move on to the real work. That's why we're here. All right, 20 seconds.
See you guys in the next 20 seconds.
Waiting for you guys. Copy it on time.
Copy it on time. Copy it on time.
So while you are copying it, we want to appreciate all the supporters here and there from the parents, our students and then everyone around me including my wife, my everyone. Thank you so much for your support to make this thing a successful one. All right, I think all of us we should be done by now. So can I clean it up? Let's move on to the real work.
Okay. Okay. Okay. Now I want to quickly remind you I want to quickly remind you of what we call angle between lines. A very simple topic. Angle between lines.
Yes. Let's go guys. Okay.
Let me have it in the comment section. A straight line is how many degree? I need response. A straight line is how many degree? Then I'm going to move on. All right. I think some people's network is fluctuating. That's all you having there and there. A straight line is how many degree?
Oh, network for some people a straight line agree.
I think the network is is having issue for some people.
Uh okay. I think I have one person back.
That's a good one. So that person needs to respond. A straight line is how many degree? A straight line is how many degree? So that we can we can be at the same page. I I I will make sure that I I teach mathematics in simplicity as simple as possible. As simple as possible. So straight line is no response yet. See there is no response.
Let me answer it for my own hand here. A straight line is 180°. Right? All of us understand that. Okay? So let now let me give you an example. We are angle between lines then not bring all those big big shape that you see in your uh in your past question that is looking scary is is because you don't know how to simplify it. I will teach you simplicity. Now a straight line is 180° right? If the straight line is 180°. Now imagine that this one is X and this one is 100°. What will be our X?
The answer in the comment section. I need your answer in the comment section if you can give me the answer. Now if a straight line is 180°, our head will be what? 180us what? 100. And our head is what? 80°.
Do you understand that? Oh, network is is Wow. Thank you. I love that someone responded. That's a good one.
That's a good one. I think this network is for some people while you're waiting for them.
Let me move on to what I call a vertical opposite angle.
All right.
Okay. So now you know how to now even if you have something like this just imagine that you have something like this. This angle on a straight line if they say this one is 100 and they say you should look for this one is still angle on a straight line. It still go on a straight line. It's as simple as that.
Or let me just hold on. I think some people are having a issue.
Sorry.
Okay. All right. I just try as much as possible to send reminder to others so you can have not on it. So now a vertically opposite angle.
You know that let me just say this.
Excuse me.
All right. Now, let me explain this thing before we move on. You know that a circle is how many degree? 360°, right?
Angle that meets at a circle. But beyond that, beyond that, you guys have to know something. Now, when you see a vertically opposite angle like this, they will be the same thing. So, if this one is 50°, this one 50° also. Are you with me? And you need to remember what I said about angle in a straight line. So if this one is 50°, this one 130°. So if this one is 130°, automatically this side will 130°.
Please take note of this. Take note of this. Very very important. A vertically opposite angle are the same thing. Now look at this one. This one and this one are the same. Are you with me? I've seen a post I think. Okay, I tweeted it. It's on my YouTube channel. It's on my YouTube channel. You can watch that question. It's one of the question. They just draw something like this. And they said something like maybe this one is 4 m + 15. I said this one is 3 m. Um, okay. Let's say this one is 7 m + 15.
Then 3 m + this. Let's say this one is minus and this one is + 75. Find a okay find a very simple very simple. Let's take it in a simplicity. Look at this question. This side and this side they are equal to each other. What will you do? Take this guy. 6 m - 15 = to what? 3 m + 75. Are you with me? That means 6 m.
If you bring this one from the right hand side to the left hand side that what? - 3 m. Then this one is 75 + 15.
If you take it from the right hand side to the left hand side that is what? 3 m = to what? 90. The Bible start by three.
Our head is what? 30°.
I'm I'm laying this foundation now. I like you guys to pay attention to this.
I'm laying this foundation now. And the foundation is that when you see a a straight line across each other. Are you with me? The vertical opposite angle are the same thing. The vertical opposite angle are what? Are the same thing. Very simple. So please quickly copy this.
quickly copy this within 20 seconds before I clean up the board. Just 20 seconds to copy it. Then we are going to move on to some I mean parallel lines.
Then we move on to some questions. All right. 20 seconds to keep to clean up the board. 19 18 17 16 If you have any question just go to the comment section and type your question now. I'm going to answer you. If you have any question do well but I encourage you guys everybody please quickly write what is on the board because it is a live meeting. If you say that you want to watch it again you not you may not be able to watch it accurately like before. All right.
That's why I encourage people to join the live class straight. Join the life class straight. We are still meeting tomorrow by the grace of God. So quickly what is on the board and a straight line is 180 is vertically opposite. They equal to each other. And I give you this question. Let me even for the question is I think 2014 something. Let me check.
2014 question. I think it's 2014.
I saw it this morning.
I saw it this morning while I was just trying to do some videos for you people while some of you are sleeping, you know, just to make sure you're working towards our success. So, please, I have copy this thing on the board. Hope I'm not blocking anybody.
You want me to shift to one side? Let me know. Just type shift to one side. Let us see the I will shift. All right. I'm waiting for you people to copy it on time. Yes, I'm correct. It's 2014.
Oh, sorry for 2010 question 10.
2010 question 10. Let's quickly do it again here.
I supposed to give you the link to watch to go and watch it on my this thing but let's just quickly solve it to prove this vertically opposite angle is just like this one very simple as ABC now 2010 question of 2010 question 10 so if you have your past question go and take it out now 2010 question 10 2010 y 2010 Then question 10 if you have a past question with you go and check it you will see it you see the question there I want to quickly solve that so that you can start interchanging those of this this thing all right so I'm going to write the question they have it like this for us they gave us this they gave us this they said this one is 4 m - 15 this one is n + 75 Five. This is a P Q and B. So find M. So it is why question 2010 question 10.
2010 question 10.
You can confirm that quickly.
You can confirm that quickly.
Sorry.
2010 question 10. So um I think some people are having network issue. I'm not having any of my students. Yeah. Okay.
Welcome back. I think one of one person is back already. That's a good one and a good turnout for us. So 2010 question 10. 2010 question 10 2010 question 10 we have something like this example I gave like I said this side and this side they are vertically opposite to each other so very simple what are you going to do just write your 4 m - 15 is equal to what n + 75 you know I've done that kind of question before that's why I can pick this kind of example so you can go to your past question for those that are just joining me go to your past question y 2010 question 10. So you will see this there and I want to quickly solve it.
How you can solve it and get answer and just get out of that listing. 4 m - 15 this side and this side they equal to each other because they are vertically opposite to each other. This side and this side they vertically opposite to each other. So that means 4 m ifus mus 15 to this place what + 15. So 3 m = 90°ide by 3 your m is what? 30°.
It's as simple as that for now. And I think you can copy the first this question and this one. Then I'll move on to angle between lines.
All right. Still waiting for some of you.
Still waiting for others. Before I move on to vertically opposite angle, then we're good to go for today.
Um and I really wish to finish this topic tonight but the response of my students um your response was very very low very very low so very very low okay all right so I think we've all copied this then let me move on to vertically opposite angle I supposed to move on to vertically opposite and if I move on to the technical aspect of it, many of you eventually struggle. So what I'm going to do is that tomorrow by the grace of God the same time 8:00 p.m. to 10 p.m. we're going to be having the second part of this geometry. But before that I want to give you an assignment that goes with uh what I've taught you today. So I'm going to clean the board and give you some assignments that goes with the one that I've explained. All right. I think we having turn out we have two people online presently now in which we have more than 250 students on our WhatsApp platform and I really wish that all of us can come together to learn. All right. So now I'm going to be giving you some assignment that goes with this um the one I've explained the first layer that I've explained. do what you do the assignment if you're on our WhatsApp platform I will encourage you to drop those answers there on our I think we have four people already on the platform so let me just quickly explain the angle between lines then we can call it a night then tomorrow we come again and continue the explanation so angle between lines I want to talk about parallel lines a line that join them together how to know your correspondent angle how to know your adjacent angle are you with me All right. So, since you guys are back, I think you can go back to work. All right.
Now, now, now think the network is frustrating for many people. Uh that's that's very very very very tonight. But we thank God. Okay.
Right. Now, so I'm going to be going to give the assignment since some people have network issue here and there. So what I just encourage you to do tomorrow, please we are starting strictly by 8:00 by 8:00 by 8:00. And our seriousness really matters. Our seriousness really matters. Do you understand that? All right. Now let me give you some assignment in line with what I've taught you today. Then tomorrow, you have a lot of topics to copy to complete rather. So please I beg you your seriousness really matters. So let me write the question on the board then you're good to go.
So let me get some questions in line of what I've taught you.
Then we call it a night then tomorrow we will meet again the same channel by 8:00 p.m. I'm seeing some question that I can quickly explain but the turnout is not really encouraging tonight and many of them may not understand it if I just jump out and see some questions that you can quickly solve now but many of our students are not presently online okay so I'm just going to write here I will here if you have a past question so let me give you this please be careful Let me give you this assignment.
Number one, let me give you number one. I'm giving assignments out now because uh many people are not online presently and you can just watch the one I've done before is accessless to you. But I'm going to give an assignment but tomorrow by 8:00 we are starting again till 10:00. The turnout is little bit low today but you're not discouraged. All right then tomorrow I'm going to take you the topic I'm I mean this topic I'm treating then we move on.
So please before tomorrow do this assignment.
2014.
Number 20.
2014 number eight.
And that's why that's why question please. That's why question.
Um, question 8. 2020 and 14 rather 20.
Okay.
2017 number 44.
2017 number 44.
Um, let me add two more to it.
Call me guys.
So please copy the questions.
Let me add one more. Wow. I've seen one.
All of us should be able to solve this.
2021 9 2021 number 26.
So these are the four questions that I'm giving as an assignment to you people.
Then tomorrow what I'm going to be teaching is angle between lines. Now imagine that we have parallel lines like this. Parallel lines are the line that will never what that will never meet. Is that correct? A line that join two par lines together is what we call transversal line. This you are going to start my class tomorrow. All right then we do some of this as example and the like transversal line. Now don't forget what I said the other time. This place and this place they are vertically opposite to each other. I love the way I'm teaching now. This place and this place they are vertically opposite to each other. This place and this place they are vertically opposite to each other also. Don't forget the vertically opposite angle. I told you the other time. Now pay attention to this. Now pay attention to this. If this place, this place and this place they are adjacent to each other. That means if this one is a, this one to what? A because they are adjacent to each other. Is that clear?
So if a is 50, let's say this one is x.
Our x to what? 50. Let me just say a= x and that's 50. Add that sense to each other.
This place and this place they are adjacent to each other. Do we understand that? Now this place and this place this place and this place A. Okay. Let me just say this one that is let's call this one Y. This Y and this place let's call this place B. They are adjacent to each other also. That means our B is equal to Y and that's adjacent to each other.
All right guys, I me don't worry. Now this place and this place they each other this place and this place to each other. They the same thing. Are you with me? Now there's a method I usually use for my students and I'm going to explain it again then tomorrow. That's where we're going to start from. This place anything that happens to this angle first angle anywhere the stone will eat this first angle will be the same place where the stone will eat this one too meaning of corresponded angle. So if this one is a now this place this place sorry that is Q and this place they corresponded to each other that means B is equal to Q that is what corresponded.
So tomorrow by the grace of God I'm going to be treating some like this that have two vertical lines I mean two transversal lines and how you can get them and the lights. So thank you so much guys. Uh we need to call it a night because number one some people truly you know there are times that you have been promising that okay we having class and some things happen and like but I I can tell you that things is under control now by the grace of God. God has helped us. The device are working very well.
You can notice that by yourself tonight.
Everything is working perfect. I still have time but I have low response tonight from the group. And so please tomorrow try to invite your friends and family. Don't that are doing Y SS1 to3 now. Then make sure that you do my assignment then you send it to me on our WhatsApp platform. Thank you so much for joining me tonight. Uh I celebrate everyone of you. Read more beyond the online class. read more, study more. I'm going to be giving you some topics in some of the other subject and the likes.
Tomorrow by the grace of God, tomorrow by the grace of God, um we having our I think according to time table I think physics and chemist like so if you not be here in my studio is maybe in our coaching center. So I'm you going to be watching live how our teacher will be teaching on other subject and the like.
Thank you so much guys for joining tonight. Don't forget to do my assignment. Your exam is coming very very very very very closer than what you thought. Thank you so much guys. See you tomorrow. Don't forget go and subscribe if you have not subscribed. Go and subscribe and tell your friend that are doubting us that the live class have started. Thank you. Have a lovely night.
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