Basic Math Quadrilaterals

Welcome back to Educator.com.0000

For the next lesson, we are going to go over quadrilaterals.0002

Remember a quadrilateral is a four-sided figure.0006

Any polygon with four sides is a quadrilateral.0009

That means the four sides has to be straight sides, and they have to be enclosed.0016

This is a type of quadrilateral.0029

Any shape that has four straight sides and no open areas is a quadrilateral.0031

Special types of quadrilaterals are listed out here.0040

The first one is a parallelogram; a parallelogram looks like this.0045

It has two pairs of opposite sides being parallel and congruent.0053

Again opposite sides are parallel and congruent.0060

Parallel means that they are slanted exactly the same way so that they will never touch.0065

If this line and this line were to keep going forever and ever, they are never going to touch.0071

That is what it means to be parallel; they are also congruent.0079

To show two sides are parallel, you can draw arrows like that.0087

One arrow with one arrow here shows that those two sides are parallel.0092

I can also say that these two lines are congruent.0097

I draw two marks like; remember that means they are congruent.0100

Then to show that these two sides are parallel and congruent, instead of drawing just one arrow0105

because one arrow is for these two, I have to draw now two arrows.0111

Now I am saying all the sides with two arrows are parallel to each other.0117

To also show that these two sides are congruent, I have to draw two marks instead of just one0126

because all the ones with one are congruent so all the ones that have two are congruent.0131

This is a parallelogram; again opposite sides are parallel and congruent.0137

These two sides are parallel and congruent; these two sides are parallel and congruent.0142

That is a parallelogram.0147

A type of parallelogram is a rectangle.0152

A rectangle is a type of parallelogram because parallelogram just has opposite sides parallel and congruent.0157

Rectangle has opposite sides parallel and congruent.0164

It is a parallelogram with four right angles.0170

It has all the properties of a parallelogram plus it has four right angles.0174

Opposite sides are parallel; these are parallel and congruent; parallel and congruent.0181

And it has four right angles; it is a special type of parallelogram.0186

The next type of parallelogram is a rhombus.0199

Rhombus, opposite sides are parallel and congruent; plus it has four congruent sides.0203

All sides are sides are congruent.0215

Again rhombus is a type of parallelogram.0220

It is not a type of rectangle; it is a type of parallelogram.0222

This is that; and then parallelogram with rhombus also.0226

The next one, square, we know what a square is.0234

But square is also a parallelogram.0238

But more specifically, it is a type of rectangle and it is a type of rhombus.0241

Square is like all of the above; why?0247

Not only does it have parallel and congruent sides,0250

it also has four right angles and it has four congruent sides.0253

The square, it has this one; it has this one; and it has this one.0260

That is a square.0273

The last one, the trapezoid; trapezoid is not a parallelogram.0280

Remember parallelogram has to have both pairs being parallel and congruent.0288

Trapezoid only has one pair; that means only this and this one are parallel.0295

One pair of parallel sides; that is the only requirement for a trapezoid.0303

Only one pair of parallel sides is trapezoid.0309

Two pairs of parallel sides and it is a parallelogram; these are obviously not parallel.0312

If these two sides were to keep going on forever, then they are going to eventually intersect.0317

Or they are going to eventually meet; so this cannot be a parallelogram.0322

Let's look at this flowchart; this right here is a parallelogram.0336

We have parallel and congruent; these two sides being parallel and congruent.0341

This is a parallelogram; there are two types of parallelograms.0349

This is a rectangle; this is a rhombus.0361

By the way, when you have more than one... rhombus is singular, when you only have one.0370

When you have more than one, it becomes rhombi; rhombi is the plural for rhombus.0376

Rectangle, rhombus; two types of parallelograms because a property of parallelogram...0383

As long as it has two pairs of opposite sides parallel and congruent, then it is a type of parallelogram.0389

This one also has that property; this one also has that property.0398

This one has to have four right angles; then it is a rectangle.0403

This one has all the parallelogram properties; plus it has four congruent sides.0408

Four right angles; four same sides.0415

Then when you combine all those properties together, it actually becomes this, a square.0427

Notice that a square has four right angles.0438

And it has four congruent sides, four same sides.0443

Square is always a rectangle; a square is always a rhombus.0450

So square is always a parallelogram.0457

Parallelograms are sometimes going to be rectangles and sometimes going to be rhombi.0463

Or it can just be a parallelogram.0470

Same thing here; rhombus can be a rhombus; or sometimes it can be a square.0473

When you look at this flowchart, if you are going downwards,0479

meaning you are comparing a parallelogram let's say to a rectangle, isn't it only sometimes?0484

Parallelogram is sometimes a rectangle because it can also be a rhombus.0489

When you are going down on the flowchart, it is going to be sometimes.0495

When you go up on the flowchart, isn't a rhombus always a parallelogram?0502

because the rhombus always has the properties of a parallelogram.0507

If you are going up on the flowchart, if you are comparing0515

like a rhombus to a parallelogram, a rhombus is always a parallelogram.0517

A square is always a rectangle because it always has four right angles.0521

A square is always going to be a rectangle; this is always.0524

Let's look at let's say a trapezoid.0533

A trapezoid doesn't fit anywhere on this flowchart.0537

Why?--because it starts off with parallelogram.0540

Parallelograms have to have two pairs of parallel sides and congruent sides.0543

Trapezoid only has one; so trapezoid goes over here to the side.0551

Parallel sides; that is a trapezoid.0557

Is a trapezoid ever going to be a parallelogram?--no, they are two different things.0570

One pair of parallel sides; two pairs of parallel sides.0575

Trapezoid, parallelogram?--never; a trapezoid to a rectangle?--never.0579

On the flowchart if you go left or right, how about rectangle with rhombus?0586

Are they ever going to be the same?--no, so this is never.0592

Again when you are going downwards, it is sometimes.0599

It is like classifying let's say animals; let's say quadrilaterals is like animals.0605

Parallelograms are types of quadrilaterals; let's say parallelograms are like dogs.0613

Parallelograms are like dogs; don't we have different types of dogs?0622

We can have Maltese; we can have Chihuahuas.0629

We can have whatever, any types of dogs.0632

The different types of dogs can go there.0637

From there, we can classify even further; that is kind of how it goes.0639

If I go as a dog, always, sometimes, never a Maltese; isn't it just sometimes?0644

Again when you go downwards, it is sometimes.0651

But then again, is a Maltese always, sometimes, never a dog?--isn't it always?0655

If I go side by side, it is going to be never.0663

Let's say over here where the trapezoid belongs, if I write birds.0666

Birds and dogs, they don't have anything to do with each other.0676

They are two different things.0679

If I ask you when is a bird a dog?--never.0681

That is how this flowchart works; this is just an example.0687

Let's do our examples; give the most exact name for the figure.0698

Here we have four congruent sides; what has four congruent sides?0704

We know that a square has four congruent sides.0708

But then again square also has to have four right angles.0712

This can be a rhombus; this can also be a parallelogram.0716

But a more exact name would be rhombus.0721

How about this one here?--this looks like a rhombus.0729

But I don't know that all four sides are congruent.0733

I know that these two are.0736

All I can say, because all I notice is that these two are congruent.0741

I do have two pairs of parallel sides; so then this is a parallelogram.0746

The last one, it looks like a rectangle; but I am not sure.0757

Here only one pair of parallel sides.0766

I don't see that any of the sides are congruent or the same.0769

No, it doesn't seem like any two sides are the same.0775

That is all I have; just that it is parallel; one pair.0778

This must be a trapezoid.0784

Just because it looks like a rectangle, it doesn't mean that it is.0790

Looks like maybe this side and this side, they are not parallel.0793

This side looks a little bit longer than this side; we can't really assume.0800

Just based on the facts, this being parallel to that and that is it, it would be a trapezoid.0804

The next one, if a parallelogram has four right angles, then it is a...0813

What do we know has four right angles?0817

We know a square has four right angles and a rectangle has four right angles.0822

But isn't a square a type of rectangle?--then this has to be a rectangle.0827

because if I say rectangle, then I am also including squares because a square is a type of rectangle.0836

A rhombus is a type of what?--yes, it is a quadrilateral.0843

But more specifically, it is a type of parallelogram.0850

If a quadrilateral has one pair of parallel sides, then it is a...0860

If it is two, then it is a parallelogram; one then it is a trapezoid.0865

The next example; always, sometimes, or never.0878

Let's see; a trapezoid is always, sometimes, or never a rectangle.0883

Remember that example where I said trapezoid is like a bird and a rectangle is a type of dog.0889

A bird is never going to be a dog.0899

It is going side by side on the flowchart.0902

It was trapezoid here; you know let me write it in red.0905

The flowchart starts off as quadrilaterals; we have trapezoids here; we have parallelograms here.0916

Parallelograms, the two types are rectangles and the rhombus.0938

These two have a square; here is your flowchart.0954

Again if you are going side by side, meaning if there is no arrows connecting them, then it is never.0962

Quadrilaterals is like saying animals.0971

Trapezoids is a type of animal; it is like a bird.0974

Parallelograms are like dogs; they branch out to the different types.0978

We said Chihuahuas and Maltese or whatever you want to say.0983

This can be, I don't know, maybe a type of Chihuahua or something.0993

That is kind of the idea of the flowchart.1000

Trapezoids, the birds, can never be type of a dog; so this is never.1002

A rhombus is always, sometimes, never, a parallelogram.1012

Maltese is always, sometimes, never, a dog; isn't it always?1017

If we are going to go up, then it is always.1021

A rectangle is always, sometimes, never a square.1027

Rectangles can just be rectangle; sometimes it could be a square.1033

Is a square always, sometimes, never a rectangle?1044

Because a square is a type of rectangle, it always has to be a rectangle.1046

That is it for this lesson; thank you for watching Educator.com.1058