I students, welcome to this section where we deal with polygons and quadrilaterals, all right, now
let's get started with polygons.
What is a polygon?
A polygon is a simple closed group made up of only line segments.
What do we mean with simple?
It means that it does not cross itself.
For example, over here, you can see that in this shape, it's crossing itself right now, in this
shape, it's not crossing itself.
So this is not a politician and this is a polygon already.
And it has to be a closed group.
That is, it cannot be left open.
For example, this is open.
So therefore, this is not a polygon.
All right.
Now, let's take a few examples to see whether they are polygons or not.
Is this a polygon?
Yes, it's simple and closed.
Right.
What about this one over here?
Yes, it's simple and closed all here.
This is not a polygon because it is not simple, because it is crossing itself and this is not a polygon
because it's open.
All right.
So we have seen that polygons are simple closed curves made up of only nine segments.
So if you had a shape like this with one part, like a semicircle, then it would not be a polygon because
a polygon is made up of only nine segments.
All right.
Let's move on to classification of polygons.
Polygons are classified on the basis of number of sites or vertices.
Now, we are familiar with this.
If you have three sites, it's called a triangle.
If you have four sites, it's called a quadrilateral.
If you have five sites, it's a Pentagon, six sites.
It's called a hexagon.
Seven sided polygon is called a have taken an eight sided polygon is called an octagon.
And nine sided polygon is in Oregon.
A ten sided polygon is it again.
And it goes on like that in general.
We can say that.
And inside it, Polygon is called and Ingunn.
All right.
Now, we will see these storms quite often in many questions.
Let's move on to quadrilaterals, which are four sided polygons.
All right.
So quadrilaterals are four sided polygons.
Let's take an example over here, OK?
We have a quadrilateral over here.
Now, this region is the interior of the quadrilateral.
This is the exterior of the quadrilateral.
All right.
Now let's move on to naming this quadrilateral.
Let me name the vertices as ABCDE.
Now, I can call this as quadrilateral A, B, C, D, you can know that the bodices are taken in a
cyclic manner.
So, for example, if the quadrilateral was named like this, A, C, B, and then this would be quadrilateral
AC C.
Now note that in this case it would be wrong to call this as quadrilateral AC B because the sides have
to be taken in a cyclic manner.
You can either call it as A, B, C, D or a DCB and you can start from any vertex, for example.
You could also call it B, C, D.
All right, let's move on.
You can see that a quadrilateral has four sides, four angles, right.
And forward issus.
So one of the four sites over here, it's A, B, B, C, C and D, what are the four angles you have?
Angley angle, B angle see an angle D All right.
So we have got a fair basic understanding of what a polygon is, what are the classifications of polygons
and what is the very basics of foresighted polygon called quadrilateral?
Now let's see, what do we mean with diagonals of a polygon?
Diagonals are line segments connecting to nonconsecutive.
What pieces of a polygon?
Let's take an example.
Over here you have a rectangle.
Now this vertex and this vertex are next to each other.
They are adjacent or they are consecutive.
So if you join these two together, you do not get a diagonal.
But this vertex and this vertex is not adjacent to each other.
So they are nonconsecutive odysseys.
So if you join these two together or this vertex and this vertex together, you get diagonals.
So in this foresighted polygon, we get two diagonals.
All right, let's take another polygon.
This is a one, two, three, four, five, five sided polygon.
And we know if I decided polygons call the Pentagon, let's draw all the possible diagonals in the Pentagon.
That would be this.
Right.
We have joined this vertex with this one.
This one.
Right.
We cannot do that with this because that would be a side that is not a diagonal because these two artists
are adjacent to each other.
Similarly, this vertex is joined with this one and this one.
And in that way, you get.
Diagonals over here.
Now, what about this polygon over here?
You have one diagonal over here and you have another diagonal over here, so you have to diagonals.
Now remember, we are discussed in permutation and combination S. how to find the number of diagonals
of an incited polygon.
The formula is NC to minus in.
Right, because you have invert exists in what it says and to draw a straight line you just need two
points to selecting.
Two points out of endpoints is in two and an end sided polygon will have Insight's right.
So you need to subtract the sides because the sides are not diagonals.
And that's why the number of diagonals is given by the formula NC to minus.
And you can see permutation and combination S..
For more details in this regard.
All right.
So we have seen what the polygons we have seen different types of polygons.
We have seen very few basic things, about a quarter lateral, and we have seen what we mean with diagonals
and how to find the number of diagonals.
Now let's see what we mean with regular and irregular polygons.
A regular polygon is one in which all the sides are equal and all the angles are equal to all the sides
have to be equal and all the angles have to be equal.
Now, all the sides being equal, we call that property being equilateral and all the angles being equal.
We call that property equally angular.
So a regular polygon is equilateral as well as Igwe angular.
Now let's take the example of a square and a rectangle.
Over here we have a square and we know that all the sides of the square are equal and all the angles
are equal to 90 degrees.
Therefore, this shape that is the shape of a square is a regular polygon.
What about a rectangle in a rectangle?
We know that opposite sides are equal, but all the sides are not equal, right?
These two sides are equal and these two sides are equal.
But for it to be regular, all the sides should have equal.
So a rectangle is not regular or it's an irregular polygon.
We know that all the angles in a rectangular equal to 90 degrees.
So it is equally angular, but it is not equilateral and hence the rectangle is an irregular polygon.
So we have seen the very basics of polygons and quadrilaterals.
And now let's move on to more interesting properties.