Chapter1BasicGeometricDefinitionsB

Defines points, lines, and planes.

In this video, we're going to go through a couple examples

that will help us to make sure that we understand our basic geometric definitions.

Example A says, "What best describes San Diego, California on a globe?"

And you guys should know that San Diego is a city.

So is it a point, a line, or a plane?

So let's remember what those words mean.

A point is like a dot, this would be a line that goes on forever,

and a plane is a 2-dimensional surface that goes on forever.

So on a globe, cities are so small compared to the whole earth

that they're usually represented by a dot.

So the best way to describe San Diego, California

on a globe would just be A, a point.

Example B: "Use the picture below to answer these questions."

And we see this sort of complicated picture where there is a plane.

That's the pink thing, plane J.

There's a line going through it, there's a couple of lines

on the plane, and some points outside.

So the first part says, "List another way to label plane J."

So besides using 1 letter that clearly states

what the plane is that we're talking about,

we can always use any 3 points on the plane to name that plane.

So, for example, you could pick points A, C, and D

to name the plane, because any 3 points will always define a plane.

There's only 1 plane that will pass through points A, C and D.

All right. "List another way to label line H."

So this is line H right here,

and we can see it's labeled right there.

So if we don't want to label it line H,

we can pick any 2 points on H, which would be A, C, or B.

Pick 2 of those to label it.

So I'm just going to say line AB because those are 2 points on the line.

You could also say AC, or CB and that would be fine.

But make sure you put the line symbol on top of your letters.

C: "Are K and F collinear?"

Remember what the word collinear means?

'Co,' that prefix always means same,

and we have the word 'line' in there.

So collinear means 'same line.'

So it's really asking, "Are K and F on the same line?"

Well, I can see here that this is a line

and K and F are both on it, so yes, they are collinear.

"Are E, B and F coplanar?"

Well, it's hard to see from this,

but what you guys need to know is that 3 points are always coplanar.

There's only 1 plane that will pass through 3 points,

and there always will be a plane to pass through any 3 points.

If you had 4 points, it wouldn't be that same thing,

but with 3 points, yes.

So yes, they are coplanar.

And let's go to the last example.

Example C: "Describe the picture below using all

the geometric terms you have learned."

So that's pretty open-ended.

We just want to describe all the things that we see.

So, for example, I see plane P.

And plane P contains point D and also line AB,

so you could say that plane P contains point D

and line AB.

Besides that, we also have these other lines, lines BC and AC

which intersect the plane and pass through it.

So we could say that as a second part.

So lines BC and AC pass through the plane.

That's just 1 way that you could describe the picture.

There's other ways, but that, at least, hit on

all of the points that we see in this picture.

Hopefully, right now you feel pretty confident

with your basic geometric definitions.

Why don't you try some of the practice problems on your own?