00:02
All right, looks like we have a coordinate proof.
00:04
If a line segment joins the midpoints of two sides of a triangle, then it is parallel to the third side.
00:13
So we have an if -then statement.
00:15
If a line segment joins the midpoints of two sides.
01:07
Okay, and we want to do a coordinate proof.
01:10
So let's draw a pair of axes.
01:11
We need our x, y, coordinates.
01:17
All right, so i'm going to draw a triangle in here.
01:19
I can draw it in whatever way is most convenient for me.
01:23
And that means it's convenient to draw it right here with one of my vertices right here in the origin.
01:32
And then i just connect here.
01:36
Now in order for this to be a proof, i don't want to set specific coordinates to these points because that doesn't prove anything.
01:43
It only proves it for that one triangle.
01:46
I want to prove it for all triangles.
01:48
And so i'm going to say that this point, this coordinate up here, is 0y and this point this coordinate right here is 0x.
02:03
Actually i think what i'm going to do is i'm going to make it 02y and 02x and you'll see why that is.
02:08
It's going to make things much nicer for us.
02:11
We won't have to deal with a fraction.
02:15
So this is going to be 02y and this is going to be 0 .2x.
02:19
The reason being because i want the midpoint.
02:22
So here i want this midpoint and so this midpoint and so that this is going to be 0...