1
00:00:00,770 --> 00:00:04,070
Any pair of points can be
connected by a line segment.

2
00:00:04,070 --> 00:00:05,150
That's right.

3
00:00:05,150 --> 00:00:07,350
Connect two pairs
of black points

4
00:00:07,350 --> 00:00:10,939
in a way that creates two
parallel line segments.

5
00:00:10,939 --> 00:00:12,230
So let's see if we can do that.

6
00:00:12,230 --> 00:00:13,646
So I could create
one segment that

7
00:00:13,646 --> 00:00:16,264
connects this
point to this point

8
00:00:16,264 --> 00:00:17,680
and then another
one that connects

9
00:00:17,680 --> 00:00:20,640
this point to this point.

10
00:00:20,640 --> 00:00:22,170
And they look pretty parallel.

11
00:00:22,170 --> 00:00:23,920
In fact, I think this
is the right answer.

12
00:00:23,920 --> 00:00:26,253
If we did it another way, if
we had connected that point

13
00:00:26,253 --> 00:00:30,530
to that point and this
point to this point,

14
00:00:30,530 --> 00:00:32,590
then it wouldn't
look so parallel.

15
00:00:32,590 --> 00:00:35,822
These clearly, if they
were to keep going,

16
00:00:35,822 --> 00:00:37,280
they would intersect
at some point.

17
00:00:37,280 --> 00:00:39,930
So let me set it back up the
way I did it the first time.

18
00:00:39,930 --> 00:00:44,710
Let me make these
two points parallel.

19
00:00:44,710 --> 00:00:46,640
And these are line
segments because they

20
00:00:46,640 --> 00:00:48,340
have two end points.

21
00:00:48,340 --> 00:00:50,490
They each have two end points.

22
00:00:50,490 --> 00:00:51,810
And they continue forever.

23
00:00:51,810 --> 00:00:53,185
Well they don't
continue forever.

24
00:00:53,185 --> 00:00:56,820
They continue forever in no
directions, in zero directions.

25
00:00:56,820 --> 00:00:59,042
If it was a ray, it
would continue forever

26
00:00:59,042 --> 00:00:59,750
in one direction.

27
00:00:59,750 --> 00:01:01,860
If it's a line, it
continues forever

28
00:01:01,860 --> 00:01:03,130
past both of these points.

29
00:01:03,130 --> 00:01:04,629
In fact, it wouldn't
have end points

30
00:01:04,629 --> 00:01:06,310
because it would
just continue forever

31
00:01:06,310 --> 00:01:10,060
in both of these directions.

32
00:01:10,060 --> 00:01:12,510
Let's do one more.

33
00:01:12,510 --> 00:01:15,610
Drag the ray so it
has an endpoint at A,

34
00:01:15,610 --> 00:01:18,570
so we want to make its endpoint
at A where the ray terminates

35
00:01:18,570 --> 00:01:20,740
and goes through one of
the other black points.

36
00:01:20,740 --> 00:01:23,304
The ray should also be
parallel to the pink line.

37
00:01:23,304 --> 00:01:24,220
So I have two options.

38
00:01:24,220 --> 00:01:25,790
I could make it go
through this black point,

39
00:01:25,790 --> 00:01:27,190
but it's clearly not parallel.

40
00:01:27,190 --> 00:01:29,394
In fact, it looks
perpendicular here.

41
00:01:29,394 --> 00:01:31,310
So let's try to make it
go through this point.

42
00:01:31,310 --> 00:01:34,840
Well, yes, when I do that, it
does indeed look like my ray

43
00:01:34,840 --> 00:01:37,290
is parallel to the pink line.

44
00:01:37,290 --> 00:01:39,320
And this is a ray because
it has one endpoint.

45
00:01:39,320 --> 00:01:40,695
This is where the
ray terminates.

46
00:01:40,695 --> 00:01:41,910
It's an endpoint.

47
00:01:41,910 --> 00:01:43,580
It literally ends there.

48
00:01:43,580 --> 00:01:45,717
And it continues forever
in one direction.

49
00:01:45,717 --> 00:01:47,550
In this case, the
direction is to the right.

50
00:01:47,550 --> 00:01:48,966
It continues forever
to the right.

51
00:01:48,966 --> 00:01:52,300
So it continues forever
in one-- continues forever

52
00:01:52,300 --> 00:01:54,710
in one direction.