So if the four sides, so from parallelograms, these are, this is all in the parallelogram universe.

So a parallelogram says that opposite sides are parallel.

In a parallelogram, the opposite sides are parallel

A parallelogram, the diagonals bisect each other

The height of the parallelogram is given right over here.

And also in a parallelogram, opposite sides have the same length.

I drew the altitude outside the parallelogram.

Hey, if we have this parallelogram ABCD,

We know that quadrilateral ABCD over here is a parallelogram.

We can split our parallelogram into two triangles.

So the area of this parallelogram would be 30.

So the height of the parallelogram is a as well.

Now, what is the area of this parallelogram right over there?

What is the area of that parallelogram going to be?

The area of this parallelogram is b squared.

Then the area of this parallelogram would literally be 5 times 6.

This parallelogram tells me that opposite sides are parallel.

First of all, a rhombus is a special case of a parallelogram

Well, the area of a parallelogram is just the base times the height.

So given that, the area of a parallelogram is just the base times the height.

So if I want to find the area, the area of ABCD, the whole parallelogram.

So the area of this parallelogram right over here is going to be a squared.

So the shaded portion is the whole square minus the area of the parallelogram.

And if you look at this part right over here, it gives you a clue.

But this right over here we would call a rectangle a parallelogram, opposite sides parallel, and we have four right angles.

Find the perimeter of the parallelogram. We have a parallelogram right over here, opposite sides are parallel.

Now, the next question I have for you is, what is the area of this parallelogram that I have just constructed?

Which essentially just says that if we had a field the size and shape of this parallelogram, and we wanted to make a fence around the field that was the shape of this parallelogram, how long would that fence have to be?

And what I want to discuss in this video is a general way of finding the area of a parallelogram.

So the perimeter of this parallelogram is going to be 12 inches, plus 8 inches, plus 12 inches, plus 8 inches.

We've shown if you have a parallelogram, opposite sides are, opposite sides have the same length

Or you could've multiplied, the other way to think about it is if I were to turn the parallelogram over, it would look something like this...

The parallelogram tells us that we are somehow interfacing with the user.

So there is actually a formula for the area of a parallelogram, it's actually just the base times the height.

What I wanna do this video is prove that the opposite angles of a parallelogram are congruent

If you have a quadrilateral with two pairs of parallel sides, you are then dealing with a parallelogram.

Well, to think about that, let's redraw this part of the diagram so that the parallelogram is sitting on the ground.

I just shifted that top part of the parallelogram down. b squared is this entire area right over here.

Parallelo, parallelo parallelogram

In fact, if all four sides are equal, it has to be a parallelogram.

They can be subdivided even further if the four angles in a parallelogram are all right angles, you're dealing with a rectangle.

Let's say that we have some type of a quadrilateral and we know that the opposite sides are congruent, can we prove to ourselves that this is a parallelogram

There's other interesting things we know about the diagonals of a parallelogram, which we know all rhombi are parallelograms

So it's a parallelogram. This is a parallelogram.

And the way to think about it intuitively is imagine if we were to take this part of the parallelogram, and if we were to move it over here.