1 00:00:00,920 --> 00:00:06,210 In this video, let's discuss the exterior angle property of a triangle. 2 00:00:06,440 --> 00:00:08,350 This is a very important property. 3 00:00:08,540 --> 00:00:15,020 We start in a very easy manner so that your fundamentals are rock solid and then we progress to more 4 00:00:15,020 --> 00:00:16,040 difficult questions. 5 00:00:16,310 --> 00:00:16,730 All right. 6 00:00:16,850 --> 00:00:18,080 Let's take an example. 7 00:00:18,230 --> 00:00:20,510 We have Triangle ABC over here. 8 00:00:20,780 --> 00:00:26,370 Let's extend ABC in this way and let's mark a point over here. 9 00:00:26,750 --> 00:00:27,220 All right. 10 00:00:27,410 --> 00:00:37,770 Now, this angle over here, which is angle asid, is an exterior angle of triangle ABC at Vertex Seat. 11 00:00:37,940 --> 00:00:43,460 So at this vertex, we have formed an exterior angle by extending one of the sides. 12 00:00:43,460 --> 00:00:43,800 Right. 13 00:00:43,970 --> 00:00:46,340 So we extend ABC and we got this angle. 14 00:00:46,520 --> 00:00:49,730 And this type of an angle is called an exterior angle. 15 00:00:50,150 --> 00:00:50,680 All right. 16 00:00:51,170 --> 00:00:53,930 This type of an angle has an interesting property. 17 00:00:54,170 --> 00:00:59,060 Before we go ahead with that, let's discuss what the other angles over here are. 18 00:00:59,210 --> 00:01:03,420 You can see that ACD is adjacent to HCB, right. 19 00:01:03,440 --> 00:01:06,380 So this angle over here is adjacent to this angle. 20 00:01:06,680 --> 00:01:13,580 The other two angles are these angles, which is angle and angle B and these remaining angles. 21 00:01:13,580 --> 00:01:20,720 That is the angles which are not adjacent to the exterior angle are called interior opposite angles. 22 00:01:21,040 --> 00:01:23,450 You can see that they're interior to the triangle. 23 00:01:23,630 --> 00:01:24,020 Right. 24 00:01:24,230 --> 00:01:27,650 And they are opposite to this angle over here. 25 00:01:27,650 --> 00:01:32,940 Or you can think of it as opposite to the angle which is adjacent to the exterior angle. 26 00:01:32,960 --> 00:01:34,520 So they are not adjacent to it. 27 00:01:34,910 --> 00:01:35,380 All right. 28 00:01:35,570 --> 00:01:40,430 Now, having established the basic terminology, let's move ahead. 29 00:01:41,930 --> 00:01:51,170 As per the exterior angle, property angle, A.D. will be equal to angle a plus angle beat, and that's 30 00:01:51,170 --> 00:01:59,270 what we call the exterior angle property of a triangle that is the exterior angle is equal to the sum 31 00:01:59,660 --> 00:02:03,950 of the interior opposite angles. 32 00:02:04,370 --> 00:02:08,660 And we have seen that angle and we are the interior opposite angles. 33 00:02:08,930 --> 00:02:10,740 Now let's see why this is true. 34 00:02:11,300 --> 00:02:20,390 Let's construct a parallel line at sea, which is parallel to be so able to see right now. 35 00:02:20,600 --> 00:02:22,520 Over here, you can see that. 36 00:02:23,590 --> 00:02:31,240 E C is splitting angle ACD into two, let's mark this angler's angle way and let this be angle X. 37 00:02:31,660 --> 00:02:39,220 Now angle X will be equal to angle E because there are alternate interior angles right over here. 38 00:02:39,220 --> 00:02:43,780 Abes parallel to easy and X acting as a transposon. 39 00:02:44,030 --> 00:02:50,080 Remember, we had seen that when two lines are intersected by a transpersonal, the alternate interior 40 00:02:50,080 --> 00:02:51,110 angles are equal. 41 00:02:51,550 --> 00:03:00,070 So using this property over here, we see that angle X is equal to angle a similarly angle Y is equal 42 00:03:00,070 --> 00:03:03,760 to angle B because they are corresponding angles, right? 43 00:03:04,060 --> 00:03:09,550 Abes parallel to E, C and B is acting as the transversal. 44 00:03:09,790 --> 00:03:16,350 Therefore, this angle over here and this angle over here are corresponding angles right over here. 45 00:03:16,360 --> 00:03:22,780 Remember when two lines are parallel and there intersected by a transversal angle, one angle five are 46 00:03:22,780 --> 00:03:23,860 corresponding angles. 47 00:03:23,860 --> 00:03:24,160 Right. 48 00:03:24,310 --> 00:03:26,350 It's the same scenario over here. 49 00:03:26,560 --> 00:03:30,940 We have a parallel to see and beardie is the transposon. 50 00:03:31,090 --> 00:03:34,060 Therefore angle Y is equal to angle B. 51 00:03:34,300 --> 00:03:39,970 Now we know that angle ACDA is equal to angle X plus angle Y, right. 52 00:03:39,970 --> 00:03:46,270 You can see that from the figure angle ACD is equal to X plus white and X is equal to Angley. 53 00:03:46,270 --> 00:03:54,010 And why is equal angle B therefore we can write it as angle actis equal to angle A plus angle B or the 54 00:03:54,010 --> 00:03:59,190 exterior angle is equal to the sum of the interior opposite angles. 55 00:03:59,470 --> 00:04:02,320 Now we could have also proved this in another way. 56 00:04:02,620 --> 00:04:07,780 We will soon learn the interior angle, some property of a triangle. 57 00:04:07,930 --> 00:04:12,010 That is, if you add the three angles of a triangle, you will get 180 degrees. 58 00:04:12,250 --> 00:04:14,380 Now using that also we could have brooded. 59 00:04:14,650 --> 00:04:20,680 For example, you can see angle eight plus angle B plus angle B, C. 60 00:04:22,410 --> 00:04:29,910 Has to be 180 degrees and we will soon see that why this is so and angry A.D., which is the extent 61 00:04:30,000 --> 00:04:33,390 angle plus angle ACB. 62 00:04:34,390 --> 00:04:36,860 Also is equal to 180 degrees. 63 00:04:36,880 --> 00:04:37,690 Why is that so? 64 00:04:37,870 --> 00:04:46,540 Because these two former Leanyer pair now by equating these two, we can cancel off BSEE from here and 65 00:04:46,540 --> 00:04:46,870 here. 66 00:04:47,020 --> 00:04:54,550 And again, you will get Anglicised is equal to Angley plus angle B, so let's summarize the triangle 67 00:04:54,550 --> 00:05:01,150 property of a triangle says that the exterior angle over here we have taken 160 exterior is equal to 68 00:05:01,300 --> 00:05:04,870 the sum of the interior opposite angles.