1 00:00:03,250 --> 00:00:10,980 angles and basic constructions. On exercise number one and two we are going 2 00:00:10,980 --> 00:00:21,940 to add and subtract angles. The angles are going to be A and B. Good. With your 3 00:00:21,940 --> 00:00:28,519 compass you're going to draw a couple of arches with a different radius. This is 4 00:00:28,519 --> 00:00:39,859 very important okay so you're going to draw on a one arc okay and on B you 5 00:00:39,859 --> 00:00:52,219 change you can do slightly smaller or bigger radius B okay they you can see 6 00:00:52,219 --> 00:01:01,539 they are different. This measurement is bigger than this one. These points we are 7 00:01:01,539 --> 00:01:17,700 going to name them as 1, 2, 3, and 4. Make the point mark there as a little 8 00:01:17,700 --> 00:01:25,959 circle similar to this one you have here the same size good and now we are going to do something 9 00:01:25,959 --> 00:01:33,400 that is called transport an angle we are going to transport first we are going to transport angle a 10 00:01:33,400 --> 00:01:35,879 both on exercises 11 00:01:35,879 --> 00:01:44,659 the exercise of the adding exercise one and exercise two so in order to do that 12 00:01:44,659 --> 00:01:48,159 you will copy the radius 13 00:01:48,159 --> 00:01:50,500 A1 14 00:01:50,500 --> 00:01:54,159 this radius A12 15 00:01:54,159 --> 00:01:57,680 and you transport here 16 00:01:57,680 --> 00:02:05,359 oh, sorry, my mistake 17 00:02:05,359 --> 00:02:07,480 you transfer here 18 00:02:07,480 --> 00:02:15,310 and on exercise number 2 19 00:02:15,310 --> 00:02:18,349 you transfer the same radius 20 00:02:18,349 --> 00:02:19,629 the radius A 21 00:02:19,629 --> 00:02:23,860 so we have radius A 22 00:02:23,860 --> 00:02:27,219 on exercise number 1 23 00:02:27,219 --> 00:02:29,719 and on exercise number 2. 24 00:02:31,340 --> 00:02:32,400 And now, carefully, 25 00:02:32,900 --> 00:02:34,379 you will copy the distance 26 00:02:34,379 --> 00:02:36,800 from 1 to 2. 27 00:02:38,979 --> 00:02:40,099 So you will need to 28 00:02:40,099 --> 00:02:43,780 move the compass 29 00:02:43,780 --> 00:02:46,159 a little bit. 30 00:02:47,500 --> 00:02:48,960 Copy the distance. 31 00:02:51,289 --> 00:02:52,770 This distance, 1, 2. 32 00:02:52,770 --> 00:02:54,250 You copy with the compass 33 00:02:54,250 --> 00:02:56,050 and you transport. 34 00:02:56,050 --> 00:03:09,310 this is going to be 0.2 and this is going to be, on exercise number 2, 0.2 again. 35 00:03:09,310 --> 00:03:19,930 So we have 2, the same thing. And from 2, from the point, this distance 1-2 we 36 00:03:19,930 --> 00:03:33,949 transport here. From 2 we mark and from 2, on exercise 2, we mark again. So you will 37 00:03:33,949 --> 00:03:50,539 get the point 1 here and the point 1 here. Doing that we have copied the angle 38 00:03:50,539 --> 00:04:06,479 A. So if we connect A with 1, here, exercise number 1, and on exercise number 2, you have 39 00:04:06,479 --> 00:04:21,480 the transportation of the angle. So this triangle, A12, you have copied here and there. Good. 40 00:04:22,379 --> 00:04:26,319 We are going to continue adding and subtracting. 41 00:04:26,660 --> 00:04:30,100 So for adding, you have to add now B. 42 00:04:33,259 --> 00:04:35,079 We are going to do the same, 43 00:04:36,139 --> 00:04:40,040 but it's important that you have in mind 44 00:04:40,040 --> 00:04:50,139 that with angles, if this is zero, 45 00:04:52,959 --> 00:04:55,199 okay, this is a vertex of one angle, 46 00:04:55,199 --> 00:05:01,339 we are going to add on this direction 47 00:05:01,339 --> 00:05:10,009 and we are going to subtract in this direction. 48 00:05:11,069 --> 00:05:18,529 This is anti-clockwise, en el sentido opuesto a las agujas del reloj, o anti-horario, 49 00:05:19,149 --> 00:05:26,370 anti-clockwise, clockwise, en el sentido de las agujas del reloj, u horario. 50 00:05:26,370 --> 00:05:43,470 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. 51 00:05:43,470 --> 00:06:13,069 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. 52 00:06:13,069 --> 00:06:16,670 but on exercise number 2 we are going to copy 53 00:06:16,670 --> 00:06:19,509 from the line down 54 00:06:19,509 --> 00:06:21,750 this is really important 55 00:06:21,750 --> 00:06:23,529 again 56 00:06:23,529 --> 00:06:27,709 B4 or B3, the radius 57 00:06:27,709 --> 00:06:30,670 you copy on exercise number 1 58 00:06:30,670 --> 00:06:34,430 from the previous angle 59 00:06:34,430 --> 00:06:35,509 up 60 00:06:35,509 --> 00:06:40,709 and from the previous angle on exercise number 2 61 00:06:40,709 --> 00:06:42,089 from the previous angle 62 00:06:42,089 --> 00:07:03,589 down good doing that you will get this point will be 4 4 and on exercise number 2 this point is 63 00:07:03,589 --> 00:07:12,470 going to be 3 now you will understand okay wait a minute because now we are going to transport 64 00:07:12,470 --> 00:07:23,810 the segment 3-4, so you have to maybe decrease the radius on the compass, so you take 3-4 65 00:07:23,810 --> 00:07:43,009 with accuracy, there, 3-4, sorry, now 3-4, and we take this distance and we transport 66 00:07:43,009 --> 00:07:58,939 here so from here we have three four we transfer from four anti-clockwise to the left again three 67 00:07:58,939 --> 00:08:08,339 four this distance three four here from four very important not from one from four anti-clockwise 68 00:08:08,339 --> 00:08:28,420 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. 69 00:08:28,420 --> 00:08:42,769 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. 70 00:08:43,789 --> 00:08:57,919 Here you draw arrowhead, arrowhead, this is for an angle, and here we are going to write A plus B. 71 00:08:57,919 --> 00:09:14,600 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. 72 00:09:14,600 --> 00:09:42,559 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? 73 00:09:42,559 --> 00:09:58,070 from 3, we are going to name this point 4. Again, segment 3, 4, you transport on the 74 00:09:58,070 --> 00:10:11,919 smaller one, that one, from 3 to 4. If you connect this, the vertex you connected before, 75 00:10:11,919 --> 00:10:21,830 You have subtracted the angle B to the previous angle, A. 76 00:10:22,870 --> 00:10:30,450 Okay, so the result is this segment, this angle, sorry, this section. 77 00:10:32,409 --> 00:10:35,110 This one there. 78 00:10:36,649 --> 00:10:39,429 We are going to draw arrowheads again. 79 00:10:39,429 --> 00:10:48,179 and this distance is going to be A minus B. 80 00:10:49,639 --> 00:10:51,320 Okay, that's it. 81 00:10:51,700 --> 00:10:56,580 Let's continue with number three. 82 00:10:56,799 --> 00:10:59,059 Number three is easier. It's really easy. 83 00:10:59,820 --> 00:11:03,700 We have to divide a right angle in three equal parts. 84 00:11:03,700 --> 00:11:15,500 This is a right angle, 90 degrees, outside, inside, the four of them are 90 degrees, right angles. 85 00:11:15,840 --> 00:11:21,879 So I'm going to place here the symbol for perpendicular, so it works for the four angles. 86 00:11:21,879 --> 00:11:51,450 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? 87 00:11:51,570 --> 00:11:52,210 Your choice. 88 00:11:52,690 --> 00:11:56,490 So, we draw any radius, that's it. 89 00:11:57,230 --> 00:11:58,909 So, you will get two points. 90 00:11:58,909 --> 00:12:02,909 and with the same radius you are going to 91 00:12:02,909 --> 00:12:08,860 switch to this point with the same radius 92 00:12:08,860 --> 00:12:12,860 and draw this arc 93 00:12:12,860 --> 00:12:16,860 ok, and change again 94 00:12:16,860 --> 00:12:20,860 to the top one and draw 95 00:12:20,860 --> 00:12:24,860 this other arc 96 00:12:24,860 --> 00:12:28,860 ok, again on one 97 00:12:28,860 --> 00:12:39,259 you draw this big arc of your choice with the radius you want and change to 98 00:12:39,259 --> 00:12:47,039 this second point to one with the same radius till you cross the previous one 99 00:12:47,039 --> 00:12:59,879 and you change to the top one and do the same this way you will get points two 100 00:12:59,879 --> 00:13:22,879 three four five if you connect one with four and one with five you have the 101 00:13:22,879 --> 00:13:32,539 division into three parts because you have 30 degrees 30 degrees 30 degrees so 102 00:13:32,539 --> 00:13:39,980 you divided the right angle into 3 by the way this is the equilateral triangle 103 00:13:39,980 --> 00:13:51,740 60 degrees you have drawn you will draw later on okay so have this have in mind 104 00:13:51,740 --> 00:13:57,919 that this 1, 4, 2 is an equilateral triangle, okay? 105 00:13:58,159 --> 00:13:59,600 You will need this later. 106 00:14:01,320 --> 00:14:01,600 Good. 107 00:14:01,919 --> 00:14:06,279 And the exercise number 4, this is a mistake, 108 00:14:08,399 --> 00:14:13,259 exercise number 4 is the division of the segments, okay? 109 00:14:13,259 --> 00:14:16,960 We are going to divide the segment, this segment, AB, 110 00:14:17,620 --> 00:14:19,899 into five equal parts. 111 00:14:20,740 --> 00:14:20,940 Good. 112 00:14:20,940 --> 00:14:50,820 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, 113 00:14:50,940 --> 00:15:10,419 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. 114 00:15:10,419 --> 00:15:18,820 and on top of this line we are going to take equal measurements. If we are going 115 00:15:18,820 --> 00:15:26,259 to divide into five we will take five equal parts on the straight line. To make 116 00:15:26,259 --> 00:15:37,379 it easier for us we can use for example centimeters or something that is easy to 117 00:15:37,379 --> 00:15:41,379 transfer okay so for example it's important that you do this with the 118 00:15:41,379 --> 00:15:50,039 ruler okay so I'm going to mark for example one and a half again one and a 119 00:15:50,039 --> 00:16:02,789 half and so on so four point five six and seven point five I have here I will 120 00:16:02,789 --> 00:16:17,389 get 1, 2, 3, 4 and 5. This is the number of divisions we want. If we would like 7, I would 121 00:16:17,389 --> 00:16:25,570 take 7. This part of the line we are not going to use. And now, important, you are going 122 00:16:25,570 --> 00:16:39,799 to connect. The last division, in this case 5, you connect with B. There. That is B. And 123 00:16:39,799 --> 00:16:50,080 this is going to be the direction of the parallels. You can draw here an arrowhead, neater than 124 00:16:50,080 --> 00:17:00,779 mine please this is quite dirty and okay so this is the direction i want to copy in order to draw 125 00:17:00,779 --> 00:17:16,900 the parallels my advice is that you place a square on the on this line with the arrowhead 126 00:17:16,900 --> 00:17:25,940 something like this okay and below this one you place another ruler you can use a straight ruler 127 00:17:25,940 --> 00:17:35,500 or the bevel for example okay the other square in this is important that doesn't move at all 128 00:17:35,500 --> 00:17:43,559 okay hold still this one the straight one in this case move to the next division to four 129 00:17:43,559 --> 00:17:48,359 and draw. Move again 130 00:17:48,359 --> 00:17:53,119 to 3 and draw. Be careful 131 00:17:53,119 --> 00:17:56,680 that this one doesn't move. This is the rail 132 00:17:56,680 --> 00:18:00,640 this is your guide, so it's important that you don't move 133 00:18:00,640 --> 00:18:06,630 the guide, the rail. 134 00:18:07,750 --> 00:18:10,630 We move to 2, we trace 135 00:18:10,630 --> 00:18:14,289 we move to 1, we trace. So 136 00:18:15,190 --> 00:18:18,430 Considering these five divisions are equal, 137 00:18:19,170 --> 00:18:24,369 if we draw the parallels to this direction, we get five equal divisions. 138 00:18:25,190 --> 00:18:25,710 That's it.