Chapter 1: Basic Geometric Definitions

Definitions of a point, a line and a plane as used in geometry, also the differences between a postulate and a theorem.

In this concept, we're going to learn about basic geometric definitions.

This is so that we can make sure we know the basic vocabulary

that will help us to be successful in geometry.

The first word you need to know is a point.

And a point is basically just like a dot in space.

And you've probably heard the word point before.

The main thing you need to know about a point is that,

technically, in math, it has no length, width, or height.

So you can't measure it.

This is what a line looks like and, by definition,

a line is straight and goes on forever.

So that's why you put the arrows at the end,

to indicate that it keeps going past where I stopped drawing it,

all the way over there and forever and ever.

If we want to have our lines stop at a certain point,

like maybe it goes on forever in this way,

and then stops here, this is now called a ray.

When it only extends in 1 direction.

If we want to have it stop in both directions,

it'll look like this, and this would be called a line segment.

Those points that stop the line are called endpoints.

So a ray has 1 endpoint, and a line segment has 2 endpoints.

Any time you have a line that has points on it,

Those points are called collinear because they are on the same line.

And the word collinear has this prefix, 'co,'

which means same, and you see line in here.

So they're on the same line.

If I had another point over here, it would not be collinear with these

first 3 points, because it is not on the same line.

Now, the last basic word term that we're going to talk about is plane.

And a plane is basically a 2-dimensional surface

that extends on forever in all directions.

It's sort of hard to draw, but if you think about a piece of paper extending forever,

like a piece of paper that goes on forever, that would be a plane.

You've actually heard the word plane before, probably in algebra.

You have the normal coordinate plane as your xy axes.

This is a plane because it goes on forever.

The plane is this whole surface right here, where all the points lie.

And you know that there are points, infinite points that go on forever.

If you have points that are on the same plane--like any points

on the xy coordinate plane would be considered coplanar

because they're on the same plane.

So you might think, well, how could there be

points besides the ones on the xy plane?

Well, you could have 1 above it.

Now, that's hard for me to draw, but you could have

a 3-dimensional shape, and then you could have

multiple points that are not on the same plane.

So I'm going to draw a cube here, and on this cube

these points, they're all on the front face of the cube, are coplanar,

but the point over here on another face is not coplanar.

because it's not on the same plane as this front surface,

if we were to extend that front surface in all directions.

Now, the last thing we want to talk about is 2 words: postulate and theorem.

And you'll see these words a lot in geometry.

They mean similar things.

A postulate is something that we assume is true.

And a theorem is something that we have to prove is true.

So 1 example of a postulate would be,

If we have 2 lines that we know intersect,

and intersect means cross each other,

then those 2 lines have to intersect in a point.

This is a postulate because it's not something that we're going

to prove, we just sort of assume that it's true.

There's a similar postulate that you should know about planes.

If you have 2 planes and you know they intersect,

then they have to intersect in a line.

And that's something that you could look,

visualize by looking back at this cube.

These planes, like the top face of the cube

and the front face intersect in 1 place:

They intersect in this line.

All right. At this point, you should look at the next video,

which will go through some examples.