Monica
💫 Summary
The video teaches a trick for counting triangles in figure reasoning problems, using numbering and multiplication. The instructor explains how to count triangles in various figures and provides shortcuts for calculating the number of triangles. Examples and practice questions are given to reinforce the concepts.
✨ Highlights📊 Transcript
The video teaches how to count the number of triangles in figures, emphasizing the importance of clear basic concepts for solving advanced figures.
00:00
Emphasizes the importance of clear basic concepts for solving advanced figures.
Demonstrates a method of numbering the triangles to find the total count.
Encourages viewers to watch the video till the end for clear concepts and to share it.
To find the number of triangles in a figure, double the number written at the end of the figure.
03:03
Write numbers 1 to n where the figure ends and multiply the last number by 2 to get the number of triangles.
If there are multiple parts in the figure, find the number of triangles in each part and add them together.
Counting triangles in a figure by adding the outer and inner triangles
06:10
To count triangles, add the number of outer and inner triangles
One line means two triangles
Triangles that are already counted should not be counted again
The number of triangles in the figure is 27.
09:18
The process involves adding numbers based on the figure's symmetry.
After adding the numbers, the total becomes 27.
A shortcut method for counting the triangles is mentioned.
A shortcut trick for calculating the number of triangles inside a figure is to count the triangles in a box by multiplying the last number by 2, and then add the number of triangles outside the box.
12:22
To calculate the number of triangles inside a box, multiply the last number by 2.
Count the number of triangles outside the box separately.
Add the number of triangles inside the box and outside the box to get the total number of triangles.
The video explains how to count the number of triangles in a given figure.
15:31
To count the number of triangles in a square, multiply the number of sides by 2 and add 2.
Look for additional triangles formed by points or lines within the figure.
In the given example, there are a total of 12 triangles.
00:00Hello everyone welcome back to my channel
00:01friends, today's video is a very lotus
00:03video because friends today I am going to teach you if you find
00:05inside counting figures
00:08
00:10then this video is going to be very lotus, you will
00:12definitely watch this video till the end.
00:14Because friends, first of all I have
00:15brought basic questions for you,
00:18your concepts will become clear from basic questions,
00:19after that we will solve difficult
00:22questions as well. Friends,
00:23please watch this video till the end. If you
00:25like the video then like it and write a good comment.
00:27And friends, please share this video as much as
00:29possible. So friends, let's start
00:31today's video.
00:34So friends, first of all I will tell you
00:36how to find the number of triangles of Sikhaunga.
00:38Friends, finding the
00:39number of triangles inside the counting figure is quite
00:41difficult. When advanced level figures are
00:43asked, but friends, to solve advanced level
00:45figures, your basic
00:48concept should be clear. If the basic concept is
00:50clear, then
00:52you will be able to solve even the most difficult figures, that is why
00:54friends, I have taken all these figures. So
00:56that I can clear your concept,
00:58first of all friends, you will see here
01:00how many number of triangles are there in this figure,
01:03then you will be able to tell that this is a van,
01:05this is a tu and when a big triangle is
01:08given outside then the total triangle which is There will be three,
01:10okay, but friends, if you
01:13come to this figure, then there will be some confusion
01:15as to what will be the number of triangles and when you
01:17go to find this figure, there will be even more
01:20confusion, but friends, I have brought such software for you, no
01:23confusion only solution.
01:25Now see, what will
01:27happen here, all you have to do is to do the numbering,
01:30here van here, 2, this numbering is
01:33done, what will you do after that, by doing van plus,
01:35this will be your answer, number of
01:37triangle, there is three in this figure, okay
01:40see here. Let's take it here friends, you will
01:42write van here, you write three here, I have written this,
01:45after that friends, I will write 1 + 2 + 3,
01:48I will plus these three, then
01:50this will be A, mine will be 6 A, but
01:52in your mind, perhaps the number till will come.
01:54How did triangle six come here, here is one, two,
01:57three and here is four, but friends, if you
02:00pay attention then by mixing these two also a
02:03triangle is formed. Okay, then by mixing these two
02:05also a triangle
02:07is being formed, so there are many such. There will be triangles
02:09inside it due to which we get confused, that is why
02:11this formula has been made. Okay, now friends,
02:14look here, what will you do here,
02:16friends, you have to see how much is inside the base,
02:18here one two three four punch means one
02:22two three four punch, this is me. I have written it, now add
02:26all these plus, here friends, I have
02:28written 1 + 2 + 3 + 4 + 5, I have written 5 + 49
02:33+ content plus 515, so here I have
02:37written 50, but friends, the number of
02:39triangle is not 15. It is more than that
02:40because friends, there is a base here,
02:4315 are being built in this base, there is also a base here, so if
02:46you count the vans here, then 15 plus
02:49vans, after that friends, there is a base here too, there are
02:51vans here and here you will So
02:55friends, how much will be the number of triangles here? If
02:561 + 2 becomes 3, then here also +3 will have to be done.
02:59So friends, what will be the total. There will be total 19
03:03triangles inside this figure, so there will be such
03:06figures too. You will be able to solve it if you
03:09clear this concept. So now I am going to
03:11teach you that if you are given a figure like this,
03:13then how will you find the number of triangle?
03:15Simple, what to do, friends, you have to
03:18do the number, van tu three four,
03:21you have written where the end will be, friends,
03:24what will you do there 4 * 2 Your answer will become 8. It
03:27means double it. Let me
03:30explain it to you here. If you did
03:32not understand here, then what will you do here friends? Will you
03:34do the number when you
03:37get three four five six seven? You have written this number and
03:40end. kismen hua at pe hua hua, then
03:43coming here you will write multiply by and
03:45your answer will be that the
03:47number of triangles inside this figure will be 16.
03:50
03:58Now if it is not there then what will you do, if you
04:00do the numbering here then it will be 1 2. I have written 3 4 5 6 7 8
04:06here, friends, how much will be 8 * 2,
04:09look inside, we will
04:11number again, we will write here 1 2 3 4 5 6
04:157 8, we will write 8 * 16, we will add both of them,
04:20then here Friends, the number of
04:22triangle will be 32, so I
04:26hope that whatever I have
04:27taught you here, you have understood it. Now
04:30friends, I am taking more questions so
04:31that I can clear your concept better,
04:33so let's go friends. I have
04:36brought more questions for you, see, if
04:37such a figure comes in the exam and you are
04:39asked to find the number of triangles,
04:41then how will you find it? Friends, see,
04:44we have kept it at an advanced level, but if you have to
04:46solve it, then first of all You will have to
04:49solve this basic problem, you will have to learn it, only then you will be
04:51able to solve it. Let's
04:54start, first of all friends, you have
04:56seen in festivals, here is a
04:58triangle, here is a triangle,
05:00here is a triangle, here is
05:02how many inside a triangle. There is a triangle, there are four triangles
05:04and there is a triangle outside, so
05:07what will happen here, how much will 4 + 1 be, friends, there will be 5
05:10numbers of triangles, you have learned this
05:12and I am giving this in a shortcut trick,
05:14I see, a triangle is being formed inside,
05:15right? So one line cut means you have to count four,
05:18okay and here plus one, the
05:21triangle which will be outside has been cleared, so let's
05:23solve it with this short trick, now
05:25see, this triangle is inside, so
05:28I have put one here. So I came to
05:30know that here there will be phone numbers and
05:32triangles inside and there is one triangle, if I
05:34draw a line here and one
05:36becomes four, then I wrote four here, then
05:38what happens friends, add one triangle outside. If it
05:40happens, then how much will be 4 + 4?
05:43How much will be 8? Friends, how much will be 8 + 1. That
05:45means the number of triangles inside this figure will be
05:48nine. Friends, this much is clear. Now
05:51I am going to understand you here that here you
05:52will see how much triangle is formed inside.
05:55One has been made, see, who is going to do this
05:57?
05:59Friends, if there is one more triangle,
06:02then how much will it be, will it be four, so here I
06:04write four inside that too, and if there is a
06:07triangle, then friends, draw a line here
06:08and I am here. But I will write four,
06:10okay then what will you do friends? Let's do the
06:13plus of the outer triangle, so
06:15see here, there are 443 times, so 3 * 4 = 12, 12 +
06:181 13, so 13 will be the number of triangles in this figure.
06:21It is clear now, friends. I am
06:24going to learn this one, first of all what do you have to do,
06:26friends, look here, there is a
06:28triangle inside, okay, I have
06:31drawn a line here and here I have
06:33written four, okay then you will look inside and there
06:35is a triangle, then what will be four? So here
06:37I have written four and the outside triangle,
06:39friends, here van is 4 + 48 8 + 1 9,
06:43I have written this because friends, you will see that it is exactly
06:45from you, is there a
06:48difference here, one line here like this.
06:51A is gone and this figure has become simple, isn't it?
06:54Now what will you do friends, what is the change
06:56here, see here one line means two
07:00triangles, okay one line means two triangles,
07:03so here there are two, here there are two and here there are
07:06two. So what will be the total, here
07:09Tu Tu and Tu will be total six triangles, so
07:11here what will be 9 + 6, friends, it will be 15.
07:14Now this will come in your mind sir, you had
07:17taught earlier that this is the base, so this is one van and
07:20tu tu plus van. There should be three here,
07:22how are you telling me, but friends, when I
07:25taught you this concept of 4 + 1,
07:28
07:30this triangle was already counted within it, so
07:33why would you count it again
07:35here? You have already counted, that is
07:38why you are counting this van and you
07:41because here there is line A, so there are two
07:44triangles. You have already counted these triangles,
07:46here you have understood, that is why
07:4915 will come here, I hope
07:51friends. Whatever I have explained to you, have you understood it.
07:54Still, if you have any doubt,
07:56please do so by commenting. Now friends, I am going to take very high
07:59level questions which is
08:01very important for you, so
08:03
08:04let's start. So friends, now I am going to tell you. This is the
08:06most important question which has been
08:08asked many times in the exam. Friends, this
08:10type of figure was asked here. To find the number
08:12of triangles, how will you find it?
08:14First of all, friends, you have to see what kind of
08:16figure is here.
08:18
08:20From here you will see van tu three, from here
08:23also you will see 1 2 3 and from here also see
08:251 2 3 So there will be figures of this symmetry type
08:28so usmein how to solve how to find the number
08:29of triangles, I am going to tell you that.
08:31Pay attention, here
08:33first of all you will write the numbering here, van
08:35here you and three here, you have written it,
08:37what will you do after that friends, you
08:40will write van here, 2 here three,
08:43you have written this, after that see van
08:45of van here. I have written down here how much will be 1 + 2, that will be
08:48three and here, if you have to add three to three
08:51then what will happen, friends, it will be six, what to do
08:53after that, if you have to add these three
08:56numbers then how much will be 6 + 3, then how much will be
08:589 will be 9 + How much will 1 be? 10 and the
09:02answer has not come yet because
09:04you have to do something else. What you have to do is
09:06leave the number below. Take the first number
09:09and leave it here. You will have to
09:11follow the pattern like this and there will be more numbers. If there
09:13are, then you will have to follow the same pattern
09:16that you will leave the lower number, then people will
09:18leave, then you have to take it, then you have to leave it, this is
09:20how it has to be maintained, okay then what will
09:23you do friends, if there is three A here then
09:25you will do +3 here. And your answer will be 13. It
09:28means the number of triangles inside this figure is
09:3113, so I hope you have understood.
09:34If not, then
09:36this figure is here.
09:38Now friends, you will understand here. You will also see on this page that this
09:41is also a symmetry type figure dekhiae 1 2
09:433 4 here 1 2 3 4 here friends 1 2
09:483 4 It is done now what will I do here 1
09:522 3 4 I have written and here I will write
09:55van here You write three here and
09:58four here, I have written this, what will I do then,
10:00friends, I will write here, if there is van, then I will
10:02write van here, then friends, I will
10:04add 1 + 2 to the cross, how much will it be,
10:07friends, it will become 3, then friends, 3 in 3 +
10:10What will happen if I do six? Okay, so
10:13what will I do in six? Friends, if I do plus 4,
10:15what will be 6 + 4? It will be 10.
10:17Now if all these numbers are to be plus then what will be 10 +
10:216? What will be 16? 16 + 3 = 19 and
10:24I have written down what will be 19 + 1,
10:27what will happen after that, friends, you will
10:29follow what I taught you,
10:30first of all you will cancel the number which is below,
10:33people take this number, then you will cancel
10:35and people take this number. And what you have
10:38ticked is that you have to add the number
10:40plus, then how much will be 6 + 1, if it
10:43is 7 then you will write plus 7 and here 27 will be the
10:47answer, you mean the number of triangle in this figure is
10:5027. Now friends, I
10:53want to tell you that I also have a shortcut for this,
10:54but why have I done this
10:57method, I will also tell you the reason, the shortcut
10:59is cap, listen to it, the shortcut is that there is
11:01no need to go through so much trouble,
11:04what you have to do here. dekhiae, there is one base,
11:06okay here, dekhiae, there is second base, here,
11:09dekhiae, there is a third base, so what to do,
11:12you have to square the base,
11:14okay, then how much will be the square of three,
11:17yours will be 9, and what to do in 9, my
11:20friends. If you want to multiply by -5,
11:23then what will be 9 * 2? 18 will be -5. If you
11:26do this then your answer is 13.
11:28Here is your answer.
11:31You have to maintain this type of formula. Now you will
11:34say, remember this method. There is nothing left,
11:36tell me, I have another method, how
11:38here 1 2 3, then you have four five here and
11:42here friends 6 and 7 8 9, that means
11:46you have to count everything, are you okay with these short,
11:47what should I do after that? If there is an end in nine
11:50then it will be 9 * 2 - 5 then it will be 9 * 2 = 18 - if
11:55you do 5 then it will be 13 A,
11:58we would have seen the answer here also, here you had done the
12:01numbering, I will erase it and
12:03I will also I start from here 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12:06and 16 I have
12:14written 16, what should I do now where the
12:16end is 16 * 2, what is friends,
12:1832 is 32, after coming 32, mines. If you
12:22do five then your answer will be ejili 27 A. It
12:26seems very simple to you but friends, I have done complete
12:29research and have come up with this which
12:32comes less only in three and four. If six A is given then it does
12:35not come less and the wrong answer
12:38is A. So that's why I taught you this
12:41method, this method is such a method that
12:44if your answer is three, four, five, six or six,
12:49then it is your choice, either
12:52you understand that three or four will come,
12:55then you can do this formula. Take it and six will
12:58come, then it is okay to use this formula,
13:00so I hope you have understood,
13:02friends, now I am bringing more questions for you,
13:04so let's start,
13:05friends, I have brought high level questions for you,
13:08see if like this If a question
13:09comes in the exam and you are asked how to
13:11calculate the number of triangle, then a
13:14lot of confusion will be created, but
13:15friends, as you know,
13:18I always bring a shortcut trick for you, so
13:20friends, here I am teaching you
13:21how to calculate the number. You will find the off triangle,
13:23first of all you reduce it, forget the whole figure,
13:26remember only this figure, see this much figure, remember
13:28each
13:32thing one by one, then see it carefully, everyone
13:35will understand, then if I focus on this figure.
13:37So see this box 1 2 3
13:414 I taught you that if we
13:43say number of triangle inside such a box then the last number
13:46is four then what do we do, how much will 4 * 2 be, it will become
13:488, it is clear that
13:51means this number of inside the box.
13:53How many triangles will be there,
13:54I have written here, then friends, you will
13:56see that there is a triangle here,
13:59van and there is a triangle here, so one more one,
14:02how much will be two, you will
14:05pay attention, friends, there is a point here,
14:08a point here. There is a point so there is
14:12a point here and here is this
14:15line this line means to say in this way in this way so
14:18what did I teach you earlier when what will
14:20you teach
14:23or find in the figure, here is van and here is you. It
14:25happens and how much will be tu plus van, it will be 3,
14:27then this is the dot I have put, your
14:30three triangle form is being formed in it, so here
14:32I have written plus three, then how much will be 8 + 2, how much will be
14:3410, how much will be 10 + 3, friends, it will be
14:3713. So this will be the complete number of 13 triangles from this figure. So
14:40if you
14:43look at this figure then what will happen from here also,
14:45friends, if 13 number of triangles will come out
14:47then 13 + 13, I write here
14:5013 + 13 26 numbers of triangles now. Till
14:54I got it, after that friends,
14:56look here in the middle, then van here,
14:582 here, three here, four, so
15:01what will happen here is 4 * 2, the total number of triangles from this figure,
15:05friends, will be 8, so here I am
15:07plus 8. I will do it and your answer
15:10will be 34, you will think it is right but friends, 34 is not the
15:13right answer because friends,
15:15if you look carefully here, if you see the point here, see this point, see the point here,
15:18
15:21and if you see this point, then
15:23I have shown you this big figure exactly.
15:26You will see something like this, so when the figure is A then
15:29how do we find the number of triangle?
15:31We know how much is van and tu plus van, what is
15:33three, then what to do here,
15:35friends, in 34 you have to add plus three. Friends, if
15:38your answer comes to 37 then
15:42option C is D, then the right answer is I hope that
15:45friends, whatever I have explained, I have
15:46understood you, so come on friends, let's come in front of you friends, I have
15:49
15:51brought one more question for you, friends,
15:52you should understand such a question. So how will you solve the
15:54number of triangles, now
15:56I am going to learn that, first of all
15:58friends, you will see that if you see a
16:00square here and if the design was given like this then
16:02what would you have to do 1 2 3 4
16:05You have written this After this, friends,
16:08multiply by 4, what will happen to you, it will be 8, that means
16:10
16:12how many number of triangles will be inside this square, what will you do after that,
16:14friends, see there is a
16:16triangle on the side and here there is another triangle on this side,
16:18then how much will be 1 + 1? If you
16:20go, it will be 8 + 2. Here, but
16:23friends, where are the two triangles left?
16:26Look here, look at this one
16:28point, look at this one point, and
16:30look at the point from here, how much will this triangle be, it will
16:32become one, then look. If
16:35you look here, there is another triangle hidden, then
16:37how much will be 1 + 1, it will be 2, then friends,
16:40how much will be 10 + 2, it will be 12, so I hope
16:43friends, you have understood,
16:45this option is A, D is the right answer, so friends,
16:48and one. Question, I have brought one more question for you,
16:49friends, come with this question, this is the
16:51question, friends, you have to find the
16:52number of triangles, you have to find it,
16:54so if you look carefully,
16:56ijili, you will see three triangles,
16:58you are fine, but friends, three.
17:01Apart from the triangle, there are other triangles too,
17:03see how to do it, look here,
17:06another triangle is being formed from this joint, first reduce the
17:09three triangles that you can see easily,
17:11write them here, then see
17:13here, then I have written them. After this,
17:15friends, you will see that from this point, this point and
17:18this point, a triangle is being formed.
17:19Dekhiae, I have made it in such a way that you can
17:22understand it better. Okay,
17:23this is formed. Dekhiae,
17:28in the middle, I have written plus van here.
17:32After that, friends, you will see this.
17:34From point to this point and this point, here also
17:38a triangle is being formed, our
17:41triangle is being formed in this way, so here we will write one more
17:43van, then 3 + 1 4 + 1 5 + 1 = 6, so this is the
17:48number off inside the figure. What will be the triangle?
17:50Friends, Option C is D. Right answer is, I
17:54hope friends, whatever I have
17:55taught you in this video, you have understood.
17:57If you like this video, friends, then
17:59like it and write a good comment so
18:02that such videos can be made available to you. And we can make it
18:05and friends, don't forget to share this video.
18:07Friends, if you share then
18:09many people who do not know this thing
18:12also come to know and learn new things.
18:14So friends, you are one less person in this.
18:16Do share it as much as you can and if you are
18:19new to the channel then subscribe and press the bell icon to get the
18:22notification so that you can
18:24get new videos every day, so
18:27friends, see you again with a new video, till
18:29then keep learning, keep learning.
18:31Keep giving love like this, see you
18:33in the next video, till then remember Allah Hafiz in your prayers.
18:35
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FAQs about This YouTube Video

1. What is the trick for counting triangles in figure reasoning problems?

The trick for counting triangles in figure reasoning problems involves numbering and multiplication. By assigning numbers to the vertices of the triangles and using multiplication, the process becomes more systematic and efficient.

2. How does the instructor explain the process of counting triangles?

The instructor explains how to count triangles in various figures by breaking down the steps and providing a clear demonstration. This helps in understanding the process and applying it to different scenarios.

3. What shortcuts are provided for calculating the number of triangles?

The video provides shortcuts for calculating the number of triangles, making the process faster and more accurate. These shortcuts are useful for quickly analyzing figures and determining the total count of triangles.

4. How are examples used to reinforce the concepts of counting triangles?

Examples are used to reinforce the concepts of counting triangles by demonstrating the application of the trick in different scenarios. This practical approach helps in solidifying the understanding and mastering the techniques.

5. What type of practice questions are given in the video?

The video includes practice questions that challenge the viewers to apply the counting method to solve a variety of figure reasoning problems. These questions allow for hands-on practice and help in honing the skills of triangle counting.

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