So the lines don't, don't intersect.

It's going to go and then nope, I want to make it so it never touches.

For a rhombus, where all the sides are equal, we've shown that not only do they bisect each other but they're perpendicular bisectors of each other

Where the beams cross?

That we're either going to intersect at one place, or we're going to intersect at an infinite number of places.

And when I say bisects it, these are all

They both intersect at 0, 0.

A parallelogram, the diagonals bisect each other

The source tables intersect with the destination table

where lines meet.

So it intersects the y axis right there.

That's why I'm doing it from the right, so that the arrows don't have to cross each other.

Because it's a parallelogram, we know that the diagonals bisect each other

And any other value increases in both directions.

And just as a bit of review, if you've never seen this before, parallel lines, they never intersect.

Given AB and CD intersect at point E.

But turns out that these three I guess you can call them these three surfaces don't intersect in R4.

So parallel lines are lines that have the same slope, and they're different lines, so they never, ever intersect.

And you could then draw that line to where they intersect.

Their videos that they use are intercut with photographs of men and women and children dying in Iraq and Afghanistan and in Pakistan.

And these are the x values where you intersect the x axis.

Perpendicular lines are lines that intersect at a 90 degree angle.

you'll see lines meeting.

When I say bisecting it, it means it splits that line segment in half.

Diagonals IG and FH are drawn and intersect at point M.

But you just have to say OK, these lines will never intersect.

We already know that in a parallelogram the diagonals bisect each other.

So, what we wanna prove is that it's diagonals bisect each other

We're given a bunch of lines here that intersect in all different ways and form triangles.

It was a mistake, of course. My wires got crossed somewhere.

So just to give you a little bit of the terminology here, and we learned this in the last video, this type of system, where they don't intersect, where you have no solutions, this is an inconsistent system.

These scenes are interspersed with scenes of dead models lying around the mansion.

We could say, OK, when does this equation intersect the x axis.

And here, they're essentially the same exact line.

In the circle below, AB and CD are chords intersecting at E.

These are the points where the lines intersect the x and y axes.

You see the diagonals intersect at a 90 degree angle so we've just proved

And actually, if you were to graph this, you would see that y never actually dips below or even hits the x axis.

In the Southern region of Bangladesh, rivers and canals crisscross, creating a lush green landscape.

And maybe these healing zones can start growing, and possibly even overlap, and good things can happen.

From points B and C, draw equal arcs that intersect at D.

So the potential x values, where they intersect, x is equal to minus b, I'm just applying the quadratic equation.

And if they're not parallel to each other, they're going to intersect at a unique point.

So once again, we see that three perpendicular bisectors are intersecting at a unique point and O really is the circumcenter so, if you take any circle and you put any triangle whose vertices all sit on that circle, the center of that circle is its circumcenter

For one thing, two beams of light that cross paths don't interact with each other at all.