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Angles / Thales - Contenido educativo

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Subido el 16 de mayo de 2025 por Publio P.

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angles and basic constructions. On exercise number one and two we are going 00:00:03
to add and subtract angles. The angles are going to be A and B. Good. With your 00:00:10
compass you're going to draw a couple of arches with a different radius. This is 00:00:21
very important okay so you're going to draw on a one arc okay and on B you 00:00:28
change you can do slightly smaller or bigger radius B okay they you can see 00:00:39
they are different. This measurement is bigger than this one. These points we are 00:00:52
going to name them as 1, 2, 3, and 4. Make the point mark there as a little 00:01:01
circle similar to this one you have here the same size good and now we are going to do something 00:01:17
that is called transport an angle we are going to transport first we are going to transport angle a 00:01:25
both on exercises 00:01:33
the exercise of the adding exercise one and exercise two so in order to do that 00:01:35
you will copy the radius 00:01:44
this radius A12 00:01:50
and you transport here 00:01:54
oh, sorry, my mistake 00:01:57
you transfer here 00:02:05
and on exercise number 2 00:02:07
you transfer the same radius 00:02:15
the radius A 00:02:18
so we have radius A 00:02:19
on exercise number 1 00:02:23
and on exercise number 2. 00:02:27
And now, carefully, 00:02:31
you will copy the distance 00:02:32
from 1 to 2. 00:02:34
So you will need to 00:02:38
move the compass 00:02:40
a little bit. 00:02:43
Copy the distance. 00:02:47
This distance, 1, 2. 00:02:51
You copy with the compass 00:02:52
and you transport. 00:02:54
this is going to be 0.2 and this is going to be, on exercise number 2, 0.2 again. 00:02:56
So we have 2, the same thing. And from 2, from the point, this distance 1-2 we 00:03:09
transport here. From 2 we mark and from 2, on exercise 2, we mark again. So you will 00:03:19
get the point 1 here and the point 1 here. Doing that we have copied the angle 00:03:33
A. So if we connect A with 1, here, exercise number 1, and on exercise number 2, you have 00:03:50
the transportation of the angle. So this triangle, A12, you have copied here and there. Good. 00:04:06
We are going to continue adding and subtracting. 00:04:22
So for adding, you have to add now B. 00:04:26
We are going to do the same, 00:04:33
but it's important that you have in mind 00:04:36
that with angles, if this is zero, 00:04:40
okay, this is a vertex of one angle, 00:04:52
we are going to add on this direction 00:04:55
and we are going to subtract in this direction. 00:05:01
This is anti-clockwise, en el sentido opuesto a las agujas del reloj, o anti-horario, 00:05:11
anti-clockwise, clockwise, en el sentido de las agujas del reloj, u horario. 00:05:19
Okay, so knowing this, the direction of addition or subtraction, we have to add the angle B here, okay, on this space because we are going anti-clockwise. 00:05:26
So, let's take the distance B3 or B4, this radius, okay, radius B3, B4, and we copy from this line up, from the angle up, on exercise number 1. 00:05:43
but on exercise number 2 we are going to copy 00:06:13
from the line down 00:06:16
this is really important 00:06:19
again 00:06:21
B4 or B3, the radius 00:06:23
you copy on exercise number 1 00:06:27
from the previous angle 00:06:30
and from the previous angle on exercise number 2 00:06:35
from the previous angle 00:06:40
down good doing that you will get this point will be 4 4 and on exercise number 2 this point is 00:06:42
going to be 3 now you will understand okay wait a minute because now we are going to transport 00:07:03
the segment 3-4, so you have to maybe decrease the radius on the compass, so you take 3-4 00:07:12
with accuracy, there, 3-4, sorry, now 3-4, and we take this distance and we transport 00:07:23
here so from here we have three four we transfer from four anti-clockwise to the left again three 00:07:43
four this distance three four here from four very important not from one from four anti-clockwise 00:07:58
You will get the point 3. So we have added the angle B to A. If we connect this, we have it. That is the solution. That is the addition. 00:08:08
So, we are going to draw here a big arc that is going to work as a measurement of the whole angle, of the whole addition there. 00:08:28
Here you draw arrowhead, arrowhead, this is for an angle, and here we are going to write A plus B. 00:08:43
So we are telling, with our drawing, that this is the addition of angle A, that is here, okay, we copied A here, and B on top, addition, good. 00:08:57
We are going to do the same, but subtraction. So, with the measurement, again, 3, 4, that we have, we have before, 3, 4 again, you are going to place the compass on 3, there, mark, from 3, not from 1, ok? 00:09:14
from 3, we are going to name this point 4. Again, segment 3, 4, you transport on the 00:09:42
smaller one, that one, from 3 to 4. If you connect this, the vertex you connected before, 00:09:58
You have subtracted the angle B to the previous angle, A. 00:10:11
Okay, so the result is this segment, this angle, sorry, this section. 00:10:22
This one there. 00:10:32
We are going to draw arrowheads again. 00:10:36
and this distance is going to be A minus B. 00:10:39
Okay, that's it. 00:10:49
Let's continue with number three. 00:10:51
Number three is easier. It's really easy. 00:10:56
We have to divide a right angle in three equal parts. 00:10:59
This is a right angle, 90 degrees, outside, inside, the four of them are 90 degrees, right angles. 00:11:03
So I'm going to place here the symbol for perpendicular, so it works for the four angles. 00:11:15
And now, placing the compass, we are going to name this as a point 1, and we are going to draw any radius, not that small, not that big, okay? 00:11:21
Your choice. 00:11:51
So, we draw any radius, that's it. 00:11:52
So, you will get two points. 00:11:57
and with the same radius you are going to 00:11:58
switch to this point with the same radius 00:12:02
and draw this arc 00:12:08
ok, and change again 00:12:12
to the top one and draw 00:12:16
this other arc 00:12:20
ok, again on one 00:12:24
you draw this big arc of your choice with the radius you want and change to 00:12:28
this second point to one with the same radius till you cross the previous one 00:12:39
and you change to the top one and do the same this way you will get points two 00:12:47
three four five if you connect one with four and one with five you have the 00:12:59
division into three parts because you have 30 degrees 30 degrees 30 degrees so 00:13:22
you divided the right angle into 3 by the way this is the equilateral triangle 00:13:32
60 degrees you have drawn you will draw later on okay so have this have in mind 00:13:39
that this 1, 4, 2 is an equilateral triangle, okay? 00:13:51
You will need this later. 00:13:58
Good. 00:14:01
And the exercise number 4, this is a mistake, 00:14:01
exercise number 4 is the division of the segments, okay? 00:14:08
We are going to divide the segment, this segment, AB, 00:14:13
into five equal parts. 00:14:17
Good. 00:14:20
This is a procedure that was created by a Greek researcher from 2,000 years ago that is called Thales. Thales was a Greek guy, very clever, that discovered that if you want to divide this graphically, not with a pocket calculator, 00:14:20
Okay. You can use any straight line. Okay. This straight line you can draw with any angle. It doesn't matter. So, you can draw here, here, here, here. It doesn't matter. Okay. With any radius. 00:14:50
and on top of this line we are going to take equal measurements. If we are going 00:15:10
to divide into five we will take five equal parts on the straight line. To make 00:15:18
it easier for us we can use for example centimeters or something that is easy to 00:15:26
transfer okay so for example it's important that you do this with the 00:15:37
ruler okay so I'm going to mark for example one and a half again one and a 00:15:41
half and so on so four point five six and seven point five I have here I will 00:15:50
get 1, 2, 3, 4 and 5. This is the number of divisions we want. If we would like 7, I would 00:16:02
take 7. This part of the line we are not going to use. And now, important, you are going 00:16:17
to connect. The last division, in this case 5, you connect with B. There. That is B. And 00:16:25
this is going to be the direction of the parallels. You can draw here an arrowhead, neater than 00:16:39
mine please this is quite dirty and okay so this is the direction i want to copy in order to draw 00:16:50
the parallels my advice is that you place a square on the on this line with the arrowhead 00:17:00
something like this okay and below this one you place another ruler you can use a straight ruler 00:17:16
or the bevel for example okay the other square in this is important that doesn't move at all 00:17:25
okay hold still this one the straight one in this case move to the next division to four 00:17:35
and draw. Move again 00:17:43
to 3 and draw. Be careful 00:17:48
that this one doesn't move. This is the rail 00:17:53
this is your guide, so it's important that you don't move 00:17:56
the guide, the rail. 00:18:00
We move to 2, we trace 00:18:07
we move to 1, we trace. So 00:18:10
Considering these five divisions are equal, 00:18:15
if we draw the parallels to this direction, we get five equal divisions. 00:18:19
That's it. 00:18:25
Idioma/s:
en
Materias:
Educación Plástica y Visual
Etiquetas:
Geometría
Niveles educativos:
▼ Mostrar / ocultar niveles
  • Educación Secundaria Obligatoria
    • Ordinaria
      • Primer Ciclo
        • Primer Curso
        • Segundo Curso
Autor/es:
Publio Pérez Prieto
Subido por:
Publio P.
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
7
Fecha:
16 de mayo de 2025 - 16:41
Visibilidad:
Público
Centro:
IES PEDRO DUQUE
Duración:
18′ 28″
Relación de aspecto:
1.78:1
Resolución:
1920x1080 píxeles
Tamaño:
477.82 MBytes

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