1 00:00:00,670 --> 00:00:06,590 In this video, let's discuss the Ford test for checking congruency of triangles. 2 00:00:06,820 --> 00:00:08,110 It's called the R. 3 00:00:08,430 --> 00:00:13,720 S Rule, and this is only applicable in the case of right angled triangles. 4 00:00:13,960 --> 00:00:14,390 All right. 5 00:00:14,650 --> 00:00:18,130 Now, this rule says that if you have two triangles, right. 6 00:00:18,340 --> 00:00:20,050 And both of them should be right. 7 00:00:20,050 --> 00:00:25,060 Angled triangles or you have a right angle triangle over here and you have another right angle triangle 8 00:00:25,060 --> 00:00:25,670 over here. 9 00:00:26,090 --> 00:00:32,530 Then if the hypotenuse it stands for the hypotenuse, if the hypotenuse of these two triangles are equal 10 00:00:32,770 --> 00:00:39,490 and any side is equal to this side is equal to the side, then these two triangles are congruent. 11 00:00:39,730 --> 00:00:41,310 Now what is the hypotenuse? 12 00:00:41,530 --> 00:00:45,250 We will see more about right angled triangles further down in this course. 13 00:00:45,470 --> 00:00:48,640 But just for this video, let's quickly understand it. 14 00:00:48,940 --> 00:00:54,700 The hypotenuse is the side opposite to the angle of 90 degrees in a right angle triangle. 15 00:00:54,940 --> 00:01:00,520 So if this angle is equal to 90 degree, then this side is what we call the hypotenuse. 16 00:01:02,250 --> 00:01:07,230 And you will see that the hypotenuse is the greatest side in this triangle. 17 00:01:07,560 --> 00:01:08,030 All right. 18 00:01:08,250 --> 00:01:16,410 Now, what does the original rule say if the hypotenuse that's it's over here and any side of a right 19 00:01:16,410 --> 00:01:22,410 angle triangle this order stands on right angle triangle are equal to the hypotenuse and one side of 20 00:01:22,410 --> 00:01:26,130 another triangle, then the two triangles are congruent. 21 00:01:26,430 --> 00:01:26,860 All right. 22 00:01:26,970 --> 00:01:28,970 So we have a right angle triangle over here. 23 00:01:29,160 --> 00:01:30,620 Let's call it ABC. 24 00:01:30,870 --> 00:01:32,940 We have another right angle triangle over here. 25 00:01:33,150 --> 00:01:37,320 Let's call it BQ or that we make some space over here. 26 00:01:37,560 --> 00:01:44,070 And we have seen that these two should be right angled triangles on that angle, B, B, A, 90 degree 27 00:01:44,070 --> 00:01:46,740 angle and angle to be a 90 degree angle. 28 00:01:46,920 --> 00:01:48,960 And the hypotenuse should be equal. 29 00:01:48,990 --> 00:01:54,310 That is AC is equal to be R and any other side. 30 00:01:54,330 --> 00:01:55,860 So you have two more sides. 31 00:01:56,100 --> 00:02:03,660 But let's take BCS equal to Q are in this case, these two triangles are congruent now to check whether 32 00:02:03,660 --> 00:02:08,760 this is a valid test for congruency, just for our satisfaction. 33 00:02:08,880 --> 00:02:15,660 Let's see whether I can construct a copy of Triangle ABC if I'm just given that angle B ninety degree 34 00:02:15,870 --> 00:02:23,580 and I am given the length of X five centimeter and I'm given the length of X or centimeter. 35 00:02:23,850 --> 00:02:24,270 All right. 36 00:02:24,480 --> 00:02:26,260 We start with constricting. 37 00:02:26,260 --> 00:02:32,520 Q are equal to four centimeter, then we draw a line from Q at ninety degrees. 38 00:02:32,530 --> 00:02:34,230 So that line would go on like this. 39 00:02:34,230 --> 00:02:42,660 Right now we take our compass, put the sharp edge at point R and we cut an arc on this line with a 40 00:02:42,660 --> 00:02:48,120 diameter equal to five centimeters so that this length over here becomes five centimeter. 41 00:02:48,480 --> 00:02:55,170 Now we get point B and we join B to Q which is already joined because we have drawn this line and we 42 00:02:55,170 --> 00:02:56,440 join B to our. 43 00:02:56,460 --> 00:03:01,620 So we are able to draw a copy of Triangle ABC without any ambiguity. 44 00:03:01,770 --> 00:03:06,590 If we are just given these three pieces of information that is angle B is equal to 90 degrees. 45 00:03:06,780 --> 00:03:10,290 We are given one side and we are given the hypotenuse. 46 00:03:10,440 --> 00:03:16,190 Therefore, outages is a valid criteria to check congruency of two right angled triangles.