1 00:00:00,700 --> 00:00:04,550 In this video, let's discuss medians of a triangle. 2 00:00:04,900 --> 00:00:07,330 Say you have triangle ABC over here. 3 00:00:07,720 --> 00:00:16,930 Now let's identify point B on AC, such that AP is equal to P.c or B is the midpoint of line segment 4 00:00:16,930 --> 00:00:17,470 AC. 5 00:00:17,830 --> 00:00:18,250 All right. 6 00:00:18,460 --> 00:00:22,510 Now let's join point B to B now. 7 00:00:22,510 --> 00:00:25,320 BP is what we call a median. 8 00:00:25,690 --> 00:00:34,510 So you can see that a median is a line that goes through a vertex and it joins the midpoint of the opposite 9 00:00:34,510 --> 00:00:34,940 side. 10 00:00:35,350 --> 00:00:39,940 So it's joining a vertex to the midpoint of the opposite side. 11 00:00:39,970 --> 00:00:44,370 So over here, be the vertex and B is the midpoint of the opposite side. 12 00:00:44,380 --> 00:00:45,200 That is AC. 13 00:00:45,490 --> 00:00:49,200 So when you join BNP, you get a median already. 14 00:00:49,480 --> 00:00:51,840 Now, how many medians does a triangle have? 15 00:00:52,180 --> 00:00:54,430 You know that a triangle has three vertices. 16 00:00:54,580 --> 00:00:57,280 Therefore it will have three medians. 17 00:00:57,640 --> 00:00:59,220 Let's draw the other mutants. 18 00:00:59,800 --> 00:01:03,030 So this median that is C R, right. 19 00:01:03,250 --> 00:01:07,220 It goes through Vertex C and it. 20 00:01:08,260 --> 00:01:15,970 Joins the midpoint of the opposite side, A, B to C, right, that's here, what about AQ use the midpoint 21 00:01:15,970 --> 00:01:21,100 of B, C and Q is joined to Vertex eight, that's AQ. 22 00:01:21,100 --> 00:01:24,460 So these are the three millions of Triangle ABC. 23 00:01:24,760 --> 00:01:28,890 And you will see that the Marines also intersect at that point. 24 00:01:28,900 --> 00:01:29,290 Right. 25 00:01:29,500 --> 00:01:32,680 And this point is called the centroid. 26 00:01:33,020 --> 00:01:39,400 So we have learned that the meeting point of the altitude's of a triangle is called Auto Center. 27 00:01:39,640 --> 00:01:45,640 And over here we have learned that the meeting point of the median of a triangle is called the centroid. 28 00:01:46,680 --> 00:01:52,470 The median divides a triangle into two triangles of equal area. 29 00:01:52,710 --> 00:01:54,840 Now let's try to understand why that is. 30 00:01:55,140 --> 00:01:57,870 For example, AQ is a median, right? 31 00:01:58,050 --> 00:02:08,810 So we we're seeing that area of Triangle A, B, Q is equal to area of Triangle E, you see. 32 00:02:09,300 --> 00:02:10,320 Let's see why that is. 33 00:02:10,560 --> 00:02:15,720 Over here, we know that BQ is equal to QC because cuz the midpoint of B.C.. 34 00:02:15,840 --> 00:02:16,230 Right. 35 00:02:16,380 --> 00:02:20,580 And let's drop it perpendicular from point A to site B.C.. 36 00:02:21,570 --> 00:02:26,760 That would look like this, and this is the height of this triangle from point A, right? 37 00:02:26,910 --> 00:02:31,760 So what is the area of Abiquiu that would be half into to into it? 38 00:02:32,230 --> 00:02:37,430 And what is the area of see, that's half in do you see into it? 39 00:02:37,710 --> 00:02:39,830 And we know is look you see. 40 00:02:40,020 --> 00:02:43,160 So we see that this area is equal to this area. 41 00:02:43,170 --> 00:02:43,490 Right. 42 00:02:43,680 --> 00:02:49,590 So that's why a median divides a triangle into two triangles of equal area. 43 00:02:49,980 --> 00:02:50,420 All right. 44 00:02:50,670 --> 00:02:52,150 Now, what about the centroid? 45 00:02:52,170 --> 00:02:56,610 There is an interesting property about the centroid also that we make some space over here. 46 00:02:57,850 --> 00:03:05,320 The centroid divides each median in the ratio, two is two one, for example, over here we have the 47 00:03:05,320 --> 00:03:09,030 centroid as all now as per this property. 48 00:03:09,340 --> 00:03:17,710 What we can say is that a wall divided by OCU is divided by two by one. 49 00:03:17,710 --> 00:03:18,060 Right. 50 00:03:18,220 --> 00:03:23,560 Because this median the centroid is dividing this median equal in the ratio. 51 00:03:23,800 --> 00:03:24,530 Two is two one. 52 00:03:24,790 --> 00:03:30,340 Let's quickly revise one of the things that we've learned about medians and median is a line segment 53 00:03:30,340 --> 00:03:33,640 that joins a vertex to the midpoint of the opposite side. 54 00:03:33,790 --> 00:03:34,180 Right. 55 00:03:34,420 --> 00:03:34,830 All right. 56 00:03:34,840 --> 00:03:37,000 We have seen that a triangle has three mutant's. 57 00:03:37,270 --> 00:03:41,860 We have seen that a median divides the triangle into two triangles of equal area. 58 00:03:42,160 --> 00:03:48,850 And we have seen that the meeting point of the median is called centroid and the centroid divides each 59 00:03:48,850 --> 00:03:50,230 median in the ratio. 60 00:03:50,440 --> 00:03:51,690 Two is two one. 61 00:03:52,420 --> 00:03:52,920 All right. 62 00:03:53,380 --> 00:03:56,410 So even Bill by OPIS is equal to by one. 63 00:03:56,410 --> 00:04:00,400 And you can say see or by or is equal to two by one.