1 00:00:01,060 --> 00:00:09,060 Students in this video, let's discuss the as a rule to test congruency of two triangles, say we have 2 00:00:09,060 --> 00:00:13,360 a triangle ABC over here and let's say we have one more triangle over here. 3 00:00:13,710 --> 00:00:15,570 Let me name it as Triangle Park. 4 00:00:15,570 --> 00:00:16,020 You are. 5 00:00:17,200 --> 00:00:24,010 All right, now, Asper, this rule, if I have two sets of angles that are equal to the angle, be 6 00:00:24,010 --> 00:00:24,520 an angle. 7 00:00:24,520 --> 00:00:28,570 Q are equal and angle C and angle are equal. 8 00:00:28,870 --> 00:00:35,380 And if the included side is equal, so B C is equal to cure, then I can say that these two triangles 9 00:00:35,530 --> 00:00:36,490 are congruent. 10 00:00:36,670 --> 00:00:37,990 That's what this rule says. 11 00:00:38,300 --> 00:00:38,740 All right. 12 00:00:38,920 --> 00:00:41,670 Now let's try to understand it better over here. 13 00:00:42,310 --> 00:00:46,050 We are given two angles and one side right now. 14 00:00:46,180 --> 00:00:49,630 This rule is a valid rule to test congruency. 15 00:00:49,750 --> 00:00:57,940 If I can draw an exact copy of Triangle ABC without any ambiguity with just these three pieces of information. 16 00:00:58,210 --> 00:01:05,680 Let's take B.C., for example, has five centimeter led angle B B hundred degrees and let Anglesey four 17 00:01:05,680 --> 00:01:06,100 degrees. 18 00:01:06,310 --> 00:01:12,940 Now let's check whether, given only these three pieces of information, whether I can draw a copy of 19 00:01:12,940 --> 00:01:14,050 this triangle or not. 20 00:01:14,380 --> 00:01:14,830 All right. 21 00:01:14,980 --> 00:01:19,230 Let's start with constructing P Q, which is equal to five centimeter. 22 00:01:19,240 --> 00:01:20,560 That's just a line segment. 23 00:01:20,800 --> 00:01:24,940 Now at Q Let me draw an angle equal to 40 degree. 24 00:01:25,330 --> 00:01:27,920 So that would look like this now at P. 25 00:01:28,120 --> 00:01:34,060 Let me draw an angle which is equal to 100 degrees and you will see that they intersect at this point. 26 00:01:34,270 --> 00:01:41,800 Let me call this point as point R and you can see that we have got Triangle R, B, Q, which is an 27 00:01:41,800 --> 00:01:44,110 exact copy of Triangle ABC. 28 00:01:44,290 --> 00:01:49,870 Therefore, A.S.A. is a valid rule to check congruency of two triangles. 29 00:01:50,080 --> 00:01:51,970 Now what is it that this rule says? 30 00:01:52,270 --> 00:02:00,160 If two angles and the included side of a triangle are equal to the corresponding angles and included 31 00:02:00,160 --> 00:02:04,930 side of another triangle, then the two triangles are congruent. 32 00:02:05,620 --> 00:02:12,820 Now you will see that in some textbooks you will also have a rule called A-S, which is angle, angle 33 00:02:12,940 --> 00:02:13,980 and any side. 34 00:02:14,200 --> 00:02:16,330 The difference between these two is over here. 35 00:02:16,360 --> 00:02:19,040 This is about the included side, right? 36 00:02:19,210 --> 00:02:20,720 That's what we have mentioned over here. 37 00:02:21,010 --> 00:02:22,450 It's the included side. 38 00:02:24,580 --> 00:02:26,990 But over here, it just means any side. 39 00:02:27,160 --> 00:02:29,900 Now, these two rules are actually one and the same. 40 00:02:30,070 --> 00:02:30,670 Why is that? 41 00:02:30,670 --> 00:02:33,320 So let's say that two angles are equal. 42 00:02:33,340 --> 00:02:38,920 That's angle B, an angle B are equal to angle is 100 degrees angle CNN. 43 00:02:39,220 --> 00:02:39,870 You are equal. 44 00:02:39,880 --> 00:02:41,620 Let this be 40 degrees now. 45 00:02:41,980 --> 00:02:46,810 And it's given that this side and this side is equal right now or here. 46 00:02:46,990 --> 00:02:52,190 If two angles are equal, then definitely the third angle also will be equal, right. 47 00:02:52,390 --> 00:02:53,850 What would be angle over here? 48 00:02:53,980 --> 00:02:57,970 It's 180 minus one hundred minus 40, which is 40 degrees. 49 00:02:58,270 --> 00:03:05,380 Similarly, you will see that angle out over here is 180 minus hundred minus 40, which is equal to 50 00:03:05,380 --> 00:03:05,820 40. 51 00:03:06,100 --> 00:03:13,180 So if two angles are equal, definitely the third set of angles are also equal among the two triangles. 52 00:03:14,180 --> 00:03:22,610 So if to start with, you are given that angle is an angle, we are respectively equal to angle or an 53 00:03:22,610 --> 00:03:27,430 angle B and you are given that B C is equal to BQ, right. 54 00:03:27,650 --> 00:03:34,190 Then you can change that to SC by just finding that the third angle also will be equal and this just 55 00:03:34,190 --> 00:03:35,040 becomes equal. 56 00:03:35,040 --> 00:03:37,040 And two is it, is it. 57 00:03:37,050 --> 00:03:40,070 And it's it's almost one and the same.