WEBVTT 00:00:00.770 --> 00:00:04.070 Any pair of points can be connected by a line segment. 00:00:04.070 --> 00:00:05.150 That's right. 00:00:05.150 --> 00:00:07.350 Connect two pairs of black points 00:00:07.350 --> 00:00:10.939 in a way that creates two parallel line segments. 00:00:10.939 --> 00:00:12.230 So let's see if we can do that. 00:00:12.230 --> 00:00:13.646 So I could create one segment that 00:00:13.646 --> 00:00:16.264 connects this point to this point 00:00:16.264 --> 00:00:17.680 and then another one that connects 00:00:17.680 --> 00:00:20.640 this point to this point. 00:00:20.640 --> 00:00:22.170 And they look pretty parallel. 00:00:22.170 --> 00:00:23.920 In fact, I think this is the right answer. 00:00:23.920 --> 00:00:26.253 If we did it another way, if we had connected that point 00:00:26.253 --> 00:00:30.530 to that point and this point to this point, 00:00:30.530 --> 00:00:32.590 then it wouldn't look so parallel. 00:00:32.590 --> 00:00:35.822 These clearly, if they were to keep going, 00:00:35.822 --> 00:00:37.280 they would intersect at some point. 00:00:37.280 --> 00:00:39.930 So let me set it back up the way I did it the first time. 00:00:39.930 --> 00:00:44.710 Let me make these two points parallel. 00:00:44.710 --> 00:00:46.640 And these are line segments because they 00:00:46.640 --> 00:00:48.340 have two end points. 00:00:48.340 --> 00:00:50.490 They each have two end points. 00:00:50.490 --> 00:00:51.810 And they continue forever. 00:00:51.810 --> 00:00:53.185 Well they don't continue forever. 00:00:53.185 --> 00:00:56.820 They continue forever in no directions, in zero directions. 00:00:56.820 --> 00:00:59.042 If it was a ray, it would continue forever 00:00:59.042 --> 00:00:59.750 in one direction. 00:00:59.750 --> 00:01:01.860 If it's a line, it continues forever 00:01:01.860 --> 00:01:03.130 past both of these points. 00:01:03.130 --> 00:01:04.629 In fact, it wouldn't have end points 00:01:04.629 --> 00:01:06.310 because it would just continue forever 00:01:06.310 --> 00:01:10.060 in both of these directions. 00:01:10.060 --> 00:01:12.510 Let's do one more. 00:01:12.510 --> 00:01:15.610 Drag the ray so it has an endpoint at A, 00:01:15.610 --> 00:01:18.570 so we want to make its endpoint at A where the ray terminates 00:01:18.570 --> 00:01:20.740 and goes through one of the other black points. 00:01:20.740 --> 00:01:23.304 The ray should also be parallel to the pink line. 00:01:23.304 --> 00:01:24.220 So I have two options. 00:01:24.220 --> 00:01:25.790 I could make it go through this black point, 00:01:25.790 --> 00:01:27.190 but it's clearly not parallel. 00:01:27.190 --> 00:01:29.394 In fact, it looks perpendicular here. 00:01:29.394 --> 00:01:31.310 So let's try to make it go through this point. 00:01:31.310 --> 00:01:34.840 Well, yes, when I do that, it does indeed look like my ray 00:01:34.840 --> 00:01:37.290 is parallel to the pink line. 00:01:37.290 --> 00:01:39.320 And this is a ray because it has one endpoint. 00:01:39.320 --> 00:01:40.695 This is where the ray terminates. 00:01:40.695 --> 00:01:41.910 It's an endpoint. 00:01:41.910 --> 00:01:43.580 It literally ends there. 00:01:43.580 --> 00:01:45.717 And it continues forever in one direction. 00:01:45.717 --> 00:01:47.550 In this case, the direction is to the right. 00:01:47.550 --> 00:01:48.966 It continues forever to the right. 00:01:48.966 --> 00:01:52.300 So it continues forever in one-- continues forever 00:01:52.300 --> 00:01:54.710 in one direction.